Prepare the fillings for the rolls:
Coat the nori with rice and start the California roll:
Cut slender wedges of avocado. Try this trick: without peeling, trim the top and bottom of the avocado and cut it in segments lengthwise to the pit. Pull away the peel and then gently grasp one segment at a time and pull it off. Set the avocado aside as you prepare the cucumber and crabmeat; set them aside as well.
Stack the sheets of toasted nori and cut them in half, parallel to the lines on the seaweed (as if you were folding the longest side in half). Or crease them along the fold and then tear them apart.
Completely wrap the bamboo mat in plastic wrap (to keep the rice from sticking) and put the nori in place. Make sure the mat lies completely flat after wrapping. Lay a sheet of nori horizontally on the wrapped mat, aligned with the edge of the mat that's closest to you.
Moisten your hands with a little water to keep the rice from sticking. (Keep a bowl
of water handy). Grab a large handful of rice and toss and squeeze it lightly to form a loose oval ball.
Starting in one of the upper corners of the nori, spread the ball of rice across the top of the nori to the other side. Using both hands, "pull" the rice down to cover the nori. Spread the rice until the sheet is covered in a layer about 1/4 inch thick. Sprinkle the rice with sesame seeds or flying fish roe, if using, and pat evenly.
Add the fillings and use the mat to make a neat roll:
Holding the top corners of the rice-covered nori, flip it over. The rice will now be face down on the mat. Keep the bottom edge of the nori even with the edge of the mat closest to you.
Using your fingers, spread a pinch of wasabi across the middle of the nori. A little goes a long way, so spread lightly. You can always put more in your dipping sauce if you like more heat.
Lay equal amounts (about a small handful) of each filling ingredient down the middle of the nori. Start with a row of cucumber, overlap with the avocado slices, and then lay the crab on top.
With all eight fingers holding in the ingredients, lift the edge of the mat closest to you with your thumbs. Tucking the ingredients into the middle of the roll, bring the edge of the mat over the ingredients and straight down. Leave 1/2 inch of the nori exposed at the top edge.
Press the roll together with your thumbs and middle fingers, while pressing down on the roll with your index fingers.
Lifting just the edge of the mat, pull it forward so that the nori roll rolls another quarter turn. The seam will now be on the bottom.
Cut and serve the roll:
Press again with fingers and thumbs, molding the roll into a squared log.
Lift the mat away and transfer the roll to a cutting surface. Dip a sharp knife into a bowl of water and let a bead of water roll down the knife's blade. Cut the roll in half and then bring one half around and cut both into thirds. Stand the pieces up on a cut side.
Repeat with four of the remaining sheets of nori (you'll have one leftover) and the remaining rice and filling ingredients. Serve the sushi with pickled ginger, a small dish of soy sauce, and a little mound of wasabi.