Rinse the sushi rice under cold water until the water runs clear. Combine the rice and water in a medium saucepan and bring to a boil. Reduce heat to low, cover, and simmer for 20 minutes. Remove from heat and let it sit, covered, for 10 minutes.
In a small bowl, mix the rice vinegar, sugar, and salt until dissolved. Gently fold this mixture into the cooked rice and let it cool to room temperature.
In another bowl, combine the cooked shrimp, mayonnaise, and sriracha sauce. Adjust the sriracha to taste for desired spiciness.
Place a bamboo sushi mat on a clean surface and lay one sheet of nori on top, shiny side down. With wet hands, spread about ¾ cup of sushi rice evenly over the nori, leaving a 1-inch border at the top.
In the center of the rice, layer a few slices of avocado, some cucumber, and a generous spoonful of the shrimp mixture.
Using the bamboo mat, carefully roll the sushi away from you, pressing gently but firmly to keep the roll tight. Seal the edge of the nori with a little water.
Repeat the process with the remaining nori sheets and filling. Once all rolls are made, slice each roll into 6-8 pieces with a sharp knife.
Sprinkle sesame seeds on top of the rolls and serve with soy sauce for dipping.