Cook rice according to package directions. Transfer to large bowl; stir in vinegar, lime zest, salt and sugar. Let cool completely. Refrigerate for 1 to 2 hours or until well chilled.
Shape 1 tbsp rice into 2-inch round; transfer to parchment paper–lined tray. Repeat with remaining rice (you should have 24 rounds).
Heat 1/4 cup oil in large nonstick skillet set over high heat. In 5 batches, cook rice rounds for 3 to 4 minutes per side or until golden brown and crispy, adding oil to the pan as needed. Transfer to paper towel-lined tray.
Meanwhile, in shallow dish, combine white and black sesame seeds. Pat tuna dry with paper towel; roll in sesame seeds to coat.
Heat oil in large heavy-bottom skillet set over high heat until smoking. Cook tuna for 1 to 2 minutes per side or until seared and sesame seeds are golden. Transfer to cutting board; let stand for 5 minutes. Slice thinly into 24 slices.
In blender, purée avocado, mayonnaise and lime juice until smooth.
Top each crispy rice round with seared tuna, drizzle of avocado mayonnaise and jalapeño slice.
For a quick and easy variation, substitute smoked salmon for tuna.