Cook the sushi rice in a rice cooker or pot with water until tender and sticky, about 10 minutes. Fluff with a fork and let it cool to room temperature.
1 cup sushi rice, 1 ¼ cups water
Place a bamboo sushi rolling mat on a clean surface. Lay a sheet of nori on the mat, shiny side down.
1 ¼ cups water
Spread a thin layer of cooled sushi rice evenly over the nori, leaving a 1-inch border at the top edge.
1 ¼ cups water
Arrange julienned cucumber and sliced avocado in a line across the bottom third of the rice-covered nori.
1 ¼ cups water
Spread spicy mayo over the fillings, then carefully lift the edge of the bamboo mat and roll it tightly over the fillings, applying gentle pressure to form a compact roll. Seal the edge with a light dab of water if needed.
1 ¼ cups water
Using a sharp knife, slice the roll into 6-8 even pieces, revealing the colorful cross-section, and serve immediately.