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Fully aware I look like this rn

But I'm getting this crack theory off my chest anyway.

Penny & Oppo (stage name Groat) are the two little people who perform the horse and dog jousting tilt at the Purple Wedding. They're the children of a famous mummer (Hop-Bean) who grew up enslaved but later bought his freedom.

In ADWD while aboard the Selaesori Qhoran (The Fragant/Stinky Steward), Penny tells Tyrion:

“It was Father’s idea to do the tilts. He even trained the first pig, but by then he was too sick to ride her, so Oppo took his place. I always rode the dog. We performed for the Sealord of Braavos once, and he laughed so hard that afterward he gave each of us a… a grand gift.” [ADWD Tyrion VIII]

The dragon eggs later given to Daenerys during her wedding to Drogo are, as readers have surmised, the same three dragon eggs which Elissa Farman yoinked from Dragonstone during her and Rhaena's lesbian divorce. She sold them to the Sealord of Braavos. Despite attempts to retrieve them by Jaehaerys and Barth, they were not retrieved.

The sealord title is not hereditary but the sealord's palace is handed down. Penny says they performed for the sealord (implies it was in his palace) and that he gave each of them "a... a grand gift." She does not say what that gift is.

This is pedantic but there is a slight connotation to the word 'each' which implies 3+ in a set. Though 'each' could refer to any 2+ set, it's more likely that the word 'both' would be used in the case that there are firmly only 2 of a group. So while only Penny and Oppo performed for the Sealord, the implication seems to be that her, Oppo, and their father all received gifts, which makes 3 eggs gifts.

Again: Penny does not say what the gift is. In fact she was hesitant to even mention them, once she realized where her story was going. It sounds like she doubts some part of her story.

Tyrion does not press the issue because he thinks Penny is gearing up to ask him to do her dog/pig show with her (she is). Instead, he tries to change the subject:

“Is that where my sister found you? In Braavos?” “Your sister?” The girl looked lost. “Queen Cersei.” Penny shook her head. “She never… it was a man who came to us, in Pentos. Osmund. No, Oswald. Something like that. Oppo met with him, not me. Oppo made all of our arrangements. My brother always knew what to do, where we should go next.”

The man Oppo met was Osmund Kettleblack, obviously. And they were not in Braavos because Oppo had made the arrangements for them to leave Braavos and go to Pentos. Pentos is where Penny and Oppo somehow meet Kettleblack.

However, Littlefinger says differently:

"I had to send to Braavos for them and hide them away in a brothel until the wedding. The expense was exceeded only by the bother. It is surprisingly difficult to hide a dwarf, and Joffrey... you can lead a king to water, but with Joff one had to splash it about before he realized he could drink it. When I told him about my little surprise, His Grace said, 'Why would I want some ugly dwarfs at my feast? I hate dwarfs.' I had to take him by the shoulder and whisper, 'Not as much as your uncle will.'" [ASOS, Sansa V]

Penny and Oppo were expected to be in Braavos but for some reason they had jumped over to Pentos. Were they perhaps carrying some very hot stolen goods which Oppo feared would be discovered? As the mastermind of their operation, he might not have told Penny that the eggs were stolen; hence, her genuine confusion when recounting the story to Tyrion. She suspects the grand gifts were ill-gotten. She doesn't know.

Now to Pentos. What's in Pentos? Illyrio's mansion with Illyrio inside. Originally, Illyrio was a bravo. Later, Illyrio and Varys made their wealth stealing valuables from the rich and then selling them back:

Varys spied on lesser thieves and took their takings. I offered my help to their victims, promising to recover their valuables for a fee. Soon every man who had suffered a loss knew to come to me, whilst city’s footpads and cutpurses sought out Varys… half to slit his throat, the other half to sell him what they’d stolen. We both grew rich, and richer still when Varys trained his mice.” “In King’s Landing he kept little birds.” [ADWD, Tyrion II]

They did this by training mice/little birds to snatch items in ways other thieves could not. Why? Because these thieves had the physical advantage:

“Mice, we called them then. The older thieves were fools who thought no further than turning a night’s plunder into wine. Varys preferred orphan boys and young girls. He chose the smallest, the ones who were quick and quiet, and taught them to climb walls and slip down chimneys. He taught them to read as well. We left the gold and gems for common thieves. Instead our mice stole letters, ledgers, charts… later, they would read them and leave them where they lay. Secrets are worth more than silver or sapphires, Varys claimed. Just so. I grew so respectable that a cousin of the Prince of Pentos let me wed his maiden daughter, whilst whispers of a certain eunuch’s talents crossed the narrow sea and reached the ears of a certain king. A very anxious king, who did not wholly trust his son, nor his wife, nor his Hand, a friend of his youth who had grown arrogant and overproud. I do believe that you know the rest of this tale, is that not so?”

They were small children who could squeeze into places others, older, could not, thereby bypassing traditional security methods like 'locked and/or guarded doors.'

This isn't an advantage only children have. As a little person, Oppo's size also worked for him. Eerily similar, in the climax of A Mystery Knight (2010), we see that spymaster Bloodraven employs a comic dwarf as one of this 'thousand eyes' in order for said spy to climb up the privy shaft of a castle and steal a dragon egg from under the nose of a Blackfyre claimant:

"Who took the dragon's egg? There were guards at the door, and more guards on the steps, no way anyone could have gotten into Lord Butterwell's bedchamber unobserved." Lord Rivers smiled. "Were I to guess, I'd say someone climbed up inside the privy shaft." "The privy shaft was too small to climb." "For a man. A child could do it." "Or a dwarf," Dunk blurted. A thousand eyes, and one. Why shouldn't some of them belong to a troupe of comic dwarfs?

The question left is of course why would Illyrio want the eggs stolen? He quotes and agrees with Varys that secrets are the most valuable thing to steal, that it's best if a scene does not appear disturbed at all... but if we lock into the theory that (F)Aegon/Young Griff is Illyrio's son with Serra, the last female Blackfyre:

“How did you convince the Golden Company to take up the cause of our sweet queen when they have spent so much of their history fighting against the Targaryens?” Illyrio brushed away the objection as if it were a fly. “Black or red, a dragon is still a dragon. When Maelys the Monstrous died upon the Stepstones, it was the end of the male line of House Blackfyre.” [ADWD, Tyrion II]

...then his motivation clears up a bit. He wants them for the son he was not able to raise, and who he holds affection for:

"There is a gift for the boy in one of the chests. Some candied ginger. He was always fond of it." Illyrio sounded oddly sad. [ADWD, Tyrion III]

So why did he give them to Dany? Well this is moreso personal speculation but, taking at faith that he was being honest when he said he thought Daenerys would not survive the Dothraki Sea (and I don't see why it would be a lie) I can speculate that the eggs were a little too hot of a commodity for Illyrio to keep so close him, and it was the Dothraki that he was actually entrusting the eggs to. He gave them to the Dothraki because their gift-based economic relationship he can and does take advantage of: they will not sell the eggs, because selling is not something they do. Via Daenerys, Illyrio thinks he's bought an army for the coming invasion of Westeros. Viserys can be dispatched of cleanly at some point... at which point the eggs will be returned and can be arranged as a gift to the Golden Company, thereby Faegon.

Lastly, I want to bring back that the ship Penny, Jorah, and Tyrion are aboard is called The Stinky Steward. It's a very close play on 'the perfumed seneschal' who Daenerys is warned from, the seneschal who many theorize is come combo of the Illyrio/Varys alliance. Both Tyrion and Jorah have at some point been agents of Illyrio & Varys: Penny and Oppo are the last pieces of the puzzle, and overlooked. It reminds me of how Shae was able to see through Varys's disguise when Tyrion could not- when Tyrion couldn't see what was in plain sight!