Rinse sushi rice under cold water until clear. Combine rice with water in a saucepan, boil, reduce heat to low, cover, and simmer for 10 minutes. Let sit covered for 5 minutes before fluffing.

In a small bowl, mix rice vinegar, sugar, and salt until dissolved. Fold into slightly cooled rice with a wooden spatula.

Prepare vegetables: slice cucumber, halve avocado, shred carrot, and cut bell pepper into strips. Arrange fillings on a clean surface.

Place a nori sheet on the sushi mat, spread seasoned rice on the nori, leaving an inch at the top, and lay fillings in the center.

Starting from the bottom, roll the nori over the fillings tightly but gently. Seal the edge with a little water.

Slice the roll into 6-8 pieces with a damp, sharp knife and serve on a platter with sesame seeds, soy sauce, and wasabi.