Wash the rice in a mesh sieve under running water until water runs clear. (This helps to get rid of the excess starch and makes nice and fluffy rice. So don’t skip this step.) Place the rice in a large heavy-bottomed pot and add about 2.5 cups of cold water. Cover and bring it to a boil over high heat. Once boiled, reduce the heat to medium low and cook for 10 minutes still covered. Then turn the heat off and let it sit for another 10 minutes. Don’t remove the cover while the rice is cooking.
While rice is cooking, mix together rice vinegar, sugar and salt in a small dish. Set aside.
Once the rice is fully cooked, transfer it into a large bowl and add the rice vinegar mixture. Using a wooden spoon or a spatula, gently fold the rice to evenly spread the seasoning. Let it to cool to room temperature.
Meanwhile, cut the seaweed sheets in half. Cut the shrimp in half lengthwise. And finally cut the cucumber, avocado and red bell pepper into thin long strips. Prepare a bowl of cold water to dip your fingers to keep them wet when you handle the rice. Place the sushi mat in a large ziplock bag to prevent the rice sticking to the mat. Arrange everything around the work area.
Place the seaweed sheet rough side up on the prepared sushi mat and evenly spread about ½ cup of sushi rice on it with wet hands. Sprinkle the sesame seeds, if using, and flip it rice side down.
Place the filling on the nearest end of the seaweed sheet. To roll, hold the sushi mat with the seaweed sheet and roll it over the filling, slightly pushing the filling with your fingertips. Slightly squeeze to make a tight roll, pull on the edge of the sushi mat and continue rolling. Give another squeeze to make an even roll.
To cut the rolls, dip a very sharp knife in water and cut the roll in one motion. Serve with soy sauce and wasabi for dipping.