Cook sushi rice: Wash the rice with cold water until the water runs clear. Then add the rice and water to the rice maker. Once cooked, transfer the hot rice to a large bowl and let it cool down slightly. When it’s still very warm, stir in optional sushi vinegar (or the mixture of rice vinegar and sugar).
Prepare unagi: take the unagi from the package and bake at 360F for 10-12 minutes or according to the package instruction. Then cut it into 1/2 inch strips.
Make caterpillar rolls: Lay out the bamboo mat with an optional piece of plastic wrap on top (this will make clean up easier).
Fold the nori sheets in half and split them by hands or using a pair of scissors.
Place half of the nori sheet on top of the bamboo.
Take 3/4 cup of cooked rice and evenly spread over nori. (You can dip your hands in vinegar water to prevent sticking.)
Flip everything so that rice is facing down.
Place unagi strips and cucumber on top of the nori.
Place the thumbs underneath the bamboo mat and lift the edge up and over the filling.
Roll the bamboo mat away from you and apply some pressure to tighten it up. Keep rolling until the ends meet.
Make avocado topping: Slice a ripe avocado in half and remove the pit and skin. Then cut each piece into thin half-moon slices.
Spread the layer on the counter.
Use a large knife to lift them up and place it on top of your sushi roll.
Place plastic wrap on top, and cover with the sushi mat. Squeeze gently to shape the avocado around the roll.
Remove the mat while keep the plastic wrap, and slice the roll into bite-size pieces. Remove the plastic wrap and enjoy!