In a medium bowl, whisk together all-purpose flour (0.5 cup), cornstarch (0.25 cup), and baking powder (0.5 teaspoon); gradually whisk in ice-cold water (0.75 cup) until a smooth, thin batter forms.
Pat 2 medium soft-shell crabs dry; heat vegetable oil (4 cups) in a deep pot to 350–375°F. Dip each crab in batter, let excess drip off, then fry 3–4 minutes per side until golden; drain on a wire rack.
Combine mayonnaise (0.25 cup) and sriracha (1.5 tablespoons) in a small bowl; stir until smooth.
Place one sheet of nori shiny side down on a bamboo mat. Wet your hands, spread 0.5 cup sushi rice evenly over nori leaving a ½-inch border, then flip so rice is down. Lay half a fried crab, 0.25 English cucumber julienned, and 0.5 avocado slices across the center; drizzle spicy mayo. Roll tightly with the mat, squeezing gently.
Dip a sharp knife in water, slice each roll into 6–8 pieces, arrange on a platter, and sprinkle toasted sesame seeds (1 tablespoon). Serve immediately with soy sauce, pickled ginger, and wasabi.