One of those AU's where Izuku gets Fa Jin first before the main stockpile power of One for All except Bruce adopts gets along with Izuku way sooner
Of course Bruce has his doubts about Izuku but begins to grow fond of him when he realizes how smart Izuku actually is and isn't as naive as Bruce once thought.
But then when Bruce learns of Izuku's love of quirks and analysis of them, similar to Toshinori, Bruce sees a younger version of himself in Izuku.
He remembers when he used to do his own research on how quirks, or meta abilities in his day, worked. How late he used to stay up to try and crack the code when he didn't have martial art practice the next day. How much theories he would come up with and was itching to test out (away from prying eyes)
Bruce had forgotten. He forgot how...fun it was, that small time of bliss.
And that's what causes Bruce to open up a bit to Izuku and in turn, Izuku gets a fellow quirk nerd to ramble with.