Cut nori sheet in half and place it on bamboo mat, shiny side down. Dampen your fingers in water. Spread a thin layer of sushi rice over the seaweed, do not cover completely. Leave a 1-inch margin at the ends uncovered to seal the roll. Lay crabmeat, avocado and cucumber lengthwise. Sprinkle with sesame seeds.
To roll; slowly fold the end of the mat closest to you over the filling and tuck it in. Use medium pressure to create a compact tube. Remove the mat from around the roll, press in the loose ends and place it on a cutting board, seam side down. Using a wet, sharp knife, slice the roll in half then into 6 equal pieces. Serve with wasabi, soy sauce and pickled ginger.