Combine the rice with 1 1/4 cups cold water in a heavy-bottomed pot with a lid. Bring to a boil over high heat, stir once, then lower heat to low, cover, and cook for 20 to 22 minutes until the rice is completely tender and all the liquid is absorbed.

Empty the hot rice into a large glass or ceramic bowl. Sprinkle with 2 tablespoons rice vinegar, the sugar, and salt. Fold gently with a wooden spoon or rice paddle until the vinegar is absorbed. Taste. It should have a mild, seasoned vinegar flavor with a hint of sweetness. Cover with plastic wrap and set aside. Rice should still be slightly warm when you use it.

In a small shallow cup, combine 1/3 cup water and 1 tablespoon rice vinegar. Keep near your workstation.

Place a nori sheet on the bamboo mat. Moisten your hands with the vinegar water, scoop a scant 1 cup of rice, pat it gently together, and spread it onto the bottom two thirds of the nori sheet in a layer less than a third of an inch thick, all the way to the edges. Layer about 2 tablespoons of peanuts and a few slices of avocado across the center of the rice. Add a few basil leaves if using.

Roll from the rice end, keeping a firm grip. When you reach the bare nori, pat with a little vinegar water to seal. Press gently to seal the whole roll. Slice into 1-inch pieces with a very sharp serrated knife.

Serve with soy sauce, wasabi, and pickled ginger.