On a clean, dry cutting board, place the nori, shiny side down and the short side closest to you. Spread the rice evenly to cover the entire nori. Sprinkle sesame seeds on top. Flip the nori over so the rice side is facing down and the nori side is facing up. With the short side still closest to you, evenly stack the unagi and cucumber across the bottom third of the nori. Roll the rice covered nori.

Layer the avocado to cover the length of the roll. Place a piece of plastic wrap over the roll, then place a bamboo sushi mat over the plastic and shape into a squarish roll. Remove the mat.