Prepare the sushi rice as directed (or mix 1 cup rice with 1-1/4 cups water; bring to a boil, lower the heat, cover the pan and simmer for 20 minutes). Stir in the rice vinegar. Lay a piece of nori on a mat and sprinkle lightly with water. Spread some rice evenly over the nori, making sure to leave room on the edges (about 1/2 inch). Place avocado slices and egg pieces along the bottom edge of the rice and roll the nori like a burrito. Seal the edges with wet fingertips. Slice with a sharp knife.