Place the rice into a small saucepan and cover it with water. Let the rice soak for 20 minutes, then drain the water and return the rice to the pot.
Add the ¾ cup of water, rice vinegar, salt, and sugar, then stir and place the pot over medium heat. Bring the water to a boil, then lower the heat, cover the pot, and let it simmer for 20 minutes, until the water has been absorbed.
Remove the pot from the heat. Leave the pot covered and let it sit for 10 minutes, then uncover and fluff with a fork.
Fill a small bowl with water to keep nearby when you roll the sushi.
Place a sheet of nori on a bamboo mat, then spread half the rice in an even layer over the nori, wetting your fingers occasionally with the water to prevent sticking.
Arrange half of your avocado slices in a strip over the rice, about an inch from the edge of the nori closest to you.
Tuck the edge of the nori closest to you over the filling, then continue rolling, using the mat to keep the roll tight. See Note. Repeat the rolling process using the other nori sheet and the rest of your rice and avocado.
Use a large, sharp knife to slice each roll into 8 pieces, wiping the knife clean with a wet cloth between cuts.
Sprinkle the sushi with sesame seeds, then serve immediately with soy sauce, wasabi paste, and pickled ginger. Enjoy!