Whereas everyone else's favorite foods required research and conjecture, Zuko's post mostly builds off what we see in the show. The foods Zuko likes are inspired by multiple real-life cultures. Links to recipes will be included.
Larou (臘肉) - Also called Lap Yuk in Cantonese, is cured pork belly aka bacon. According to the old Nickelodeon ATLA page, sizzle-crisps appear to be the Fire Nation's version of bacon bits. And, according to the official Avatar cookbook, sizzle-crisps are Zuko's favorite snack. He likes their long shelf-life and versatility, which are necessities for food meant to be stored on a ship. He not only eats them on their own as a snack, but uses them as seasoning for any dishes he considers under-seasoned and bland, which is most non-Fire Nation food. As such, he always carries around a bag of "sizzle crisps", like how some people always have hot sauce on their person. He likes his larou extra peppery.
Shaved Ice - A popular summer treat in many parts of the world, Asia included. In its most basic form, shaved ice is frozen water or milk, topped with a sweet syrup. Shaved ice brings back bittersweet memories for Zuko, reminding him of fun times spent at Ember Island with his family. Zuko's favorite flavors are guava and watermelon. He normally eats a pretty basic version in public, but will go all out with toppings when no one's watching.
Jook - Jook is the Cantonese name for rice porridge and the term Iroh uses when serving it to Zuko. Considering Zuko's tendency to push himself too hard, it's likely that the prince had a good number of bed-rest days during his banishment. As such, I think Iroh is quite used to preparing jook for his nephew. While Zuko initially didn't appreciate being "babied" (from his perspective), he comes to associate jook with his uncle's love for him. Rice porridge is eaten all over Asia.
Inihaw Na Bangus - Tagolog for "Grilled Milkfish", this is a popular fish dish in the Philippines. The milkfish is stuffed with flavorful ingredients, scored, and grilled over a fire. During the book 1 episode, "The Warriors of Kyoshi", Zuko is shown being served what looks to be this dish by his ship's cook. I feel that Zuko would have a love-hate relationship with this meal. He genuinely loves eating it, but it was also served to him very often, due to the availability of the fish while out at sea. Thus, Zuko went through cycles of eating it constantly, and then not even wanting to see it for months at a time. After the war, it became a meal he'd have about once a week.
Sea cucumber sashimi - As I mentioned in a previous post, "sea slug" is a more antiquated name for the sea cucumber. In ATLA, smoked sea slug is served as commoner's food, while parts of the sea slug are served raw to the wealthy. In real life, sea slug/cucumber is actually an expensive delicacy that's served raw in Japan and Korea. Considering Zuko's willingness to steal high quality food in Book 2, I always felt that he probably has a rather refined palette. "Sea slug" sashimi was probably the dish he missed most from the FN palace. He liked dipping it in soy sauce mixed with chili paste.
Tea - I'm sure we all saw this coming. Under Iroh's influence, Zuko comes to appreciate tea. While not the connoisseur that his uncle is, he does enjoy winding down with a mellow jasmine tea at the end of the day.
Also, I think we can all agree that Zuko would never eat a turtle-duck. ^_^
