Wash and drain rice 4 to 5 times in a medium sized pot. Cover rice with water and allow it to soak for 20 minutes. Drain.
Pour in 2 cups (480ml) water. Drop the kombu into the pot and place pot on stove over medium heat. Just as water is about to boil, remove kombu. Place the lid back on and allow water to come to a boil. Reduce heat to medium low and let rice cook for about 8 to 10 minutes or until all water is absorbed.
Turn off heat and remove pot without opening the lid. Allow rice to sit for 10 minutes before handling.
Combine vinegar, sugar, and salt in a small bowl. Stir until sugar and salt dissolve.
Transfer rice to a moistened sushi tub or large shallow bowl. Pour vinegar mixture evenly over the rice. Gently mix in the vinegar mixture with a rice paddle in a cutting motion. Do not mash. Turn the rice with the paddle and fan as you go along. This will help the rice absorb the vinegar and give it a glossy look.
Making the rolls and serving
Wrap sushi mat completely with plastic shrink wrap. Tape down the ends of the plastic on the other side of the mat.
Place a sheet of nori on your work surface. Moistened your hands and spread an even layer of vinegared rice with the help of a rice paddle onto nori. Sprinkle toasted sesame seeds over the rice.
Turn the rice covered nori over onto the plastic covered sushi mat. Spread another thin layer of rice about half way up the nori.
Make a groove in the center of the rice and place 3 strips of avocado, 3 shrimps, and a few slices of pickled ginger along the groove.
Holding down the filling with your fingers, lift the mat with your thumbs and start rolling forward while retracting the mat backwards. Use the mat to help shape the roll. Repeat until all rice is used up.
Moisten knife and slice each sushi roll about ¾ inch thick. Serve with a small dollop of wasabi.