To make sushi rice, rinse rice in cold water until water is almost clear. Cook rice in rice cooker according to manufacturer’s directions. Turn rice out into a flat, shallow bowl. Mix with a rice paddle or spatula, using gently cutting and folding motions, while fanning rice with a fan or piece of cardboard. When rice is no longer steaming, add sushi vinegar a little at a time (use two to three tablespoons vinegar per cup of cooked rice) while continuing to mix and fan until rice is seasoned to taste. When rice is room temperature, cover with a damp towel or plastic wrap. Do not refrigerate.
To make oshinko-maki (pickled vegetable rolls), place 1 sheet nori, shiny side down, on a bamboo sushi mat. With dampened fingers, place about 1-1/2 cups rice on nori, gently spreading it with your fingers to cover the nori, leaving about 3/4-inch uncovered at top. Place 4 strips cucumber and 4 strips pickle across center of rice. Roll up from bottom, using mat to assist. Repeat to make 2 rolls. With a sharp knife, cut each roll into 6 pieces, wiping knife with a damp cloth between each cut.
To make California rolls, mix surimi or crabmeat with mayonnaise. Place 1 sheet nori, shiny side up, on a bamboo sushi mat (wrap mat in plastic wrap to prevent rice from sticking). With dampened fingers, place about 1-1/2 cups rice on nori, gently spreading it with your fingers to cover the nori. Sprinkle rice with 2 tablespoons sesame seeds. Turn nori and rice over so that rice is on the bottom. Place 1/3 cup surimi or crab, 3 slices avocado and 3 strips cucumber across center of rice. Roll up from bottom, using mat to assist. Repeat to make 2 rolls. With a sharp knife, cut into each roll into 6 pieces, wiping knife with a damp cloth between each cut.
Arrange sushi, cut sides up, on a decorative platter; garnish with pickled ginger and wasabi paste. Serve soy sauce in small bowls for dipping.
