Place the rice into a colander and rinse until the water runs clear.
Add the rice and 2 cups of water into a medium saucepan over high heat. Bring to a boil, uncovered. Once it begins to boil, reduce the heat to low and cover. Cook for 15 minutes. Remove the pot from the heat and let stand, covered, for 10 minutes.
Combine the rice vinegar, sugar and salt in a small bowl and heat in the microwave for 20-30 seconds. Transfer the rice to a large bowl and add the vinegar mixture. Fold thoroughly to combine. Allow the rice to cool to room temperature
Place one sheet of nori on a flat surface and press approximately 1/3-1/2 cup rice across the surface of the nori, going all the way to the edges. This is easiest if your fingers are slightly damp.
Place a piece of plastic wrap over the rice covered nori and invert on top of a sushi rolling mat so that the seaweed side is up.
Place 2 shrimp, 2 strips of cucumber and 2 slices of avocado along one side of the nori.
Pick up the edge of the rolling mat closest to the shrimp mixture and tightly roll up the sushi.
Press approximately 2 teaspoons of sesame seeds into the rice on the sushi roll.
Using a sharp knife, slice the sushi then serve immediately.