Prepare the sushi rice by combining 1 cup uncooked rice in a covered saucepan with 1 1/2 cups water. Bring to a boil and then simmer for 15 to 20 minutes, or until the water has been absorbed. Remove from the heat and let stand covered, for 10 more minutes. Mix in the seasoned rice vinegar and let cool to room temperature.
Peel the carrot and cucumber and slice into long, thin pieces. Cut the avocado in half, remove the pit and peel off the outside. Cut the avocado into thin slices.
Place 1 nori sheet, rough-side facing up, on a bamboo mat or sheet of waxed paper. Using a bamboo paddle or spoon, flatten a 1/8-inch thick layer of rice over the nori, leaving the furthest edge from you bare. Keep the paddle or spoon wet, this helps spread the rice easily. Lay equal amounts carrot, cucumber, avocado, and faux chicken strips horizontally across the rice, about a 1/4-length of the nori away from you. A small amount wasabi can also be spread across the rice.
To roll the sushi:
Start with thumbs underneath the closest edge of the bamboo mat or wax paper. Lift up with thumbs, and use the index and middle fingers to push the top edge of the nori down and around the ingredients. Cook's Note: Keeping fingers wet will help prevent them from sticking to the nori. Pull the bamboo mat or waxed paper away from the nori as you roll away from yourself. Once the sushi is rolled tightly, use wet fingers to moisten the outside of the bare edge of the nori, this will help seal the roll. Repeat all steps with the remaining ingredients.
Use a serrated knife to cut the sushi roll into 1-inch thick slices. Serve with soy sauce and wasabi, if using.