Prepare a bowl of cold water to wet your hands. (This will prevent the rice from sticking to your fingers)For sushi rice:Dissolve the sugar in the rice vinegar.In a fine-mesh strainer, rinse the rice with running water until the water is clear.In a saucepan, weigh the rice and add 1.5 times its volume in water.Bring to a boil and cook for 15 minutes over low heat, covered.Let the rice cool.Pour the sugar-vinegar mixture over the rice and mix with a bamboo spatula. Lay a bamboo mat or a sheet of food plastic wrap on a work surface.Place a layer of sparse and even rice on the full surface.Cut a sheet of seaweed. Draw a line of wasabi across the width.Place thick pieces of avocado lengthwise.Roll everything up, closing the roll.Sprinkle with sesame seeds. Refrigerate until serving.