Heat 2 inches of vegetable oil to 350°F. Whisk flour, cornstarch, baking powder, and 1/2 tsp salt, then stir in ice-cold water until just combined. Pat shrimp dry, dip in batter, and fry in batches 2 to 3 minutes until pale gold and crisp. Drain on a rack.

Dissolve sugar and 1 tsp salt in rice vinegar. Fold the mixture into warm sushi rice with a cutting motion, fanning to cool until glossy and slightly sticky.

Place a nori sheet shiny-side down on a bamboo mat. With wet hands, spread half the rice over the nori, leaving a 1-inch strip bare at the top. Arrange 4 shrimp, half the cucumber, and half the avocado across the lower third.

Lift the mat edge and fold the nori over the fillings, tucking tightly. Roll forward using the mat to press the cylinder firm, moisten the bare nori strip with water, and seal the roll. Repeat with remaining ingredients.

With a wet, sharp knife, slice each roll into 8 rounds, wiping the blade between cuts. Stir mayonnaise and sriracha together, drizzle over the slices, and top with sesame seeds if using. Serve immediately.