Rinse sushi rice under cold water until water runs clear. Drain.
Combine rice and water in a pot. Bring to a boil, then reduce heat to low, cover, and simmer for 18 minutes.
Remove from heat and let stand, covered, for 10 minutes.
In a small bowl, mix rice vinegar, sugar, and salt until dissolved.
Fold the vinegar mixture into the hot rice using a cutting motion. Spread rice on a sheet pan to cool to room temperature.
Shred imitation crab into a bowl. Add mayonnaise, sriracha (if using), and green onions. Mix well.
Slice cucumber lengthwise into thin strips (about 1/8-inch thick) using a mandoline or vegetable peeler. You'll need about 12 strips.
Place a nori sheet shiny side down on a work surface (or bamboo mat). Spread about ¾ cup of rice evenly over nori, leaving a 1-inch strip at the top edge.
Lay 3 cucumber strips horizontally across the center of the rice. Spoon about 2 tablespoons of crab mixture over the cucumbers.
Using the mat or your fingers, lift the bottom edge of the nori and roll tightly over the filling, tucking as you go. Press gently to seal.
Moisten the top edge of nori with a dab of water to seal the roll completely.
Repeat with remaining nori and filling.
Using a sharp knife, slice each roll into 8 pieces. Wipe knife clean between cuts for neat slices.
Arrange on a platter, garnish with sesame seeds, and serve with soy sauce and pickled ginger.