Wash the rice in a fine mesh sieve under cold water until the water runs clear.
Combine the rice and 1 cup water in a covered pot or rice cooker. Bring to a boil, reduce heat, simmer 15 minutes, then remove from heat and let it steam for 10 minutes more.
Stir together rice vinegar, sugar, and salt until dissolved. Gently fold into the warm rice and cover with a damp towel.
Mix shredded imitation crab with mayonnaise in a small bowl.
Slice avocado and cucumber into thin strips.
Place a sheet of nori shiny-side down on a bamboo sushi mat. Wet hands to prevent sticking.
Spread a thin layer of rice over the nori, leaving a 1-inch border. Sprinkle optional sesame seeds.
Flip the nori so rice side is down. Arrange crab mix, avocado, and cucumber along the near edge.
Roll firmly but gently into a tight log using the mat. Seal the edge with water.
Use a sharp, wet knife to slice the roll into 8 pieces and serve with soy sauce, pickled ginger, and wasabi.