Place cooked rice in a container and add rice vinegar, sugar and salt. Mix well.
Wrap bamboo mat with plastic wrap and have a bowl of water mixed with a little rice vinegar on the side.
Lay a nori sheet with the shiny side facing down on the bamboo mat. Add 1 cup of rice to the center of the nori sheet and wet your fingers with vinegar water.
Spread the rice using your fingers, evenly across the nori sheet.
Sprinkle about ½ teaspoon sesame seeds onto the rice evenly across.
Turn the nori sheet over so the rice is facing down. Move the nori sheet close to the edge of the bottom of the bamboo mat.
Thinly slice the cucumber (as long as possible).
Place cucumber horizontally on top of the nori.
Grab the bottom edges of the mat with your thumbs and hold on to the toppings with your other fingers.
Roll into a tight cylinder and lift the edges of the bamboo mat to prevent it from rolling into the roll together with the filling. The mat should look like the letter C from the side as you roll forward. Keep rolling forward using a little pressure and let go when the roll is done.
Cut the roll in half and then into thirds.
Serve with soy sauce and wasabi.