Cut the nori sheets in half horizontally (with the shorter side facing you) so that you have ten smaller rectangles. Cut the cucumber and avocado into thin strips. Leave the surimi sticks whole, cut them into small sticks, or chop them into fine pieces. Set aside.
Add an equal amount of the white and black sesame seeds to a small bowl and mix together. Add some water to another small bowl. Set aside.
Cover the bamboo sushi rolling mat in plastic wrap. Place a sheet of nori on the bottom half of the mat with the rough side facing up.
Add a generous amount of sushi rice on top of the nori. Dip your fingertips in the water and press the rice evenly over the nori, edge to edge. Sprinkle the rice with sesame seeds if desired.
Fold the top half of the rolling mat over the nori sheet and flip it over. Unfold the mat. Now, the rice side should be facing down.
Place 2 of the surimi sticks, some cucumber, and some avocado in the line across the bottom half of the nori.
Using the rolling mat, roll the sushi away from you. Keep the filling tightly in place. Add some pressure to the roll once it's rolled all the way to help everything stick and make it easy to cut.
Wet the blade of a sharp knife and cut the roll in half. Cut those pieces in half again and then cut those pieces in half, for a total of 8 equally sized pieces.
Arrange on a platter with small bowls of soy sauce for dipping and wasabi paste and pickled ginger on the side. Serve immediately.
Notes
If you're chopping up the surimi sticks into tiny pieces, I recommend mixing the imitation crab with 3-4 tablespoons of Kewpie mayo. This will help keep it together and add some flavor. You'll have to eyeball how much crab to use, or you can divide it into 10 equal-ish portions ahead of time to make things easier when you're ready to assemble the rolls.