Line an 8x8-inch baking dish with plastic wrap. Add the cooked sushi rice and spread evenly. Press another layer of plastic wrap on top and refrigerate overnight to set.
The next day, remove the rice block from the dish and slice into small rectangles (bite-size pieces).
Heat ½ inch avocado oil in a skillet to 375°F.
Working in batches, fry the rice pieces until golden brown and crisp on both sides, flipping halfway through. Transfer to a paper towel–lined plate to drain.
In a bowl, combine diced salmon, Kewpie mayo, sriracha, soy sauce, sesame oil, and lime juice. Stir gently to combine. Taste and adjust heat or acidity if desired.
Top each crispy rice square with a spoonful of spicy salmon, followed by a dollop of Roe caviar.
Finish with thinly sliced chives and serve immediately.