Rinse the sushi rice under cold water until the water runs clear.
In a medium saucepan, combine the rinsed rice and water. Bring to a boil, then reduce heat to low, cover, and simmer for 18-20 minutes until the rice is tender.
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. Allow the rice to cool to room temperature.
In another bowl, combine the sriracha sauce and mayonnaise to create a spicy sauce. Add the cooked shrimp and toss until well coated.
To assemble the sushi stacks, use a round mold or a small cup. Start by layering a spoonful of sushi rice at the bottom, followed by a layer of spicy shrimp, then a layer of avocado and cucumber. Repeat the layers until the mold is full, finishing with a layer of sushi rice on top.
Carefully remove the mold and sprinkle sesame seeds and chopped green onions on top.
Serve immediately with nori squares on the side for wrapping.