Cook the sushi rice according to packet instructions.
While the rice is still hot, gently mix in sushi vinegar, salt, and sugar using a flat rice paddle, using a slicing motion to avoid crushing the grains.
Transfer the seasoned rice to a wide dish and allow it to cool completely.
In a small bowl, mix all the ingredients for the Japanese mayonnaise. Set aside.
Cut the crabsticks into thin strips. Mix half of them with a little Japanese mayonnaise until well combined.
Prepare the remaining fillings: slice avocado, cucumber, and any other ingredients you are using.
Fold one nori sheet in half and cut in half. Place one half on a plate, shiny side down.
Spoon some rice onto the top left corner in a rough triangular shape and gently flatten.
Layer your chosen fillings over the rice.
Fold the bottom left corner over the fillings, then roll diagonally into a cone shape.
Sprinkle with sesame seeds.
Serve immediately with soy sauce, wasabi, and sushi ginger.