Cook the Sushi Rice:
Rinse the sushi rice under cold water until the water runs clear. Combine the rice with 1 1/4 cups of water in a rice cooker or pot. Cook according to the rice cooker instructions, or bring to a boil, cover, and simmer for 12-15 minutes until the rice is fully cooked. Remove from heat and let it sit, covered, for 10 minutes.

Season the Rice:
While the rice is cooling, mix the rice vinegar, sugar, and salt in a small bowl. Microwave for 15-20 seconds or heat on the stovetop until the sugar and salt are dissolved. Once the rice has cooled slightly, gently fold the vinegar mixture into the rice. Let the seasoned rice cool to room temperature.

Prepare the Fillings:
While the rice is cooling, prepare your fillings. Slice the ripe avocados in half, remove the pit, and scoop out the flesh. Cut the avocado into thin strips. Julienne the cucumber and carrot into thin strips, if using. Set aside.

Assemble the Sushi Rolls:
Lay a bamboo sushi mat on a flat surface, and place a sheet of nori (shiny side down) on top of the mat. Spread a thin layer of cooled sushi rice evenly over the nori, leaving about 1 inch at the top free from rice. Be sure to press the rice gently but firmly to stick to the nori.

Add the Fillings:
Place a few slices of avocado, cucumber, and carrot (if using) along the center of the rice.

Roll the Sushi:
Carefully lift the edge of the bamboo mat closest to you and roll it over the fillings, pressing gently to form a tight cylinder. Continue rolling until you reach the top of the nori, then wet the exposed edge of the nori with a little water to seal the roll.

Slice the Rolls:
Use a sharp knife to slice the roll into 6-8 pieces, wiping the knife with a damp cloth between cuts to ensure clean slices.

Serve:
Arrange the avocado sushi rolls on a plate. Serve with soy sauce, pickled ginger, and wasabi on the side for dipping.