Rinse the sushi rice under cold water until the water runs clear, then combine it with the water in a pot. Bring to a boil, reduce heat to low, cover, and cook for 20 minutes until the water is absorbed.

Mix the rice vinegar, sugar, and salt in a small bowl until dissolved. Transfer the cooked rice to a large bowl and gently fold in the vinegar mixture. Let the rice cool to room temperature.

Place one nori sheet on a bamboo mat with the shiny side down. Spread half the rice evenly over the nori, leaving a 1-inch border at the top. Arrange half the carrot and cucumber matchsticks in a line across the center, then add half the avocado slices beside them.

Lift the edge of the mat closest to you and roll the nori over the filling, pressing gently to shape a tight cylinder. Continue rolling until the seam seals. Repeat with the second nori sheet and remaining ingredients.

Use a sharp knife to slice each roll into 6 pieces. Arrange the pieces on a plate and sprinkle black sesame seeds over the tops. Serve with soy sauce on the side.