Cover your sushi mat (both sides) with plastic wrap.
Don't worry about wasting plastic - cover it up securely so that the sushi mat doesn't stick out from the sides or shift around. Use 2 sheets if it's not wide enough.
Fold the nori sheet in half to separate. Cut the crab sticks lengthwise so that the red part is evenly distributed on both pieces. Remove the pit from the avocado and cut it into 12 lengthwise wedges.
Remove the stem end of the cucumber, and slice it into fourths. Remove any seeds.
Lay a sheet of nori horizontally. Evenly spread the sushi rice. Make a mounded lip on the edge of the far-side.
Quickly flip over the nori and sushi rice. Make sure the lip remains on the far-side. Line the near-side of the nori and rice to the edge of your sushi mat.
Place 2 slices of the avocado on the center, then place the imitation crab sticks on top with the red side facing downwards. You can also use 4 slices of avocado if you'd like.
Roll it up from the front as you press the ingredients together. You can see in this photo that I forgot to line the rice to the edge of my sushi mat.
When you finish wrapping, the end of the sushi mat should meet the lip of the rice. So, press the rice of the lip slightly until any excess sticks out. This serves as a glue.
Remove the end of the sushi mat. Roll the sushi roll and squeeze tightly to secure the rice together. Now roll the sushi again to shape.
Sprinkle the roasted sesame seeds on top.
Leave it in a cool place for a while, then slice into sixths. The result will look nicer if you wipe your knife with a damp cloth between each slice.
Story Behind this Recipe
I was making American-style sushi for a few months as a sushi chef at a sushi counter. Since it's been a while now, I posted this recipe for my own reminder; I was starting to forget a few important points.
If you press the lip too much in Step 9, the resulting rice won't turn out evenly. If you place 4 slices of avocados with 2 horizontal pairs, the sushi will have a nice round (or square) filling.