While the rice cools, you can make the simmered shiitake mushrooms and prep the veggies. Slice the cucumber thinly. Use a box grater to shred the carrots and thinly slice the avocados. Begin by laying a large piece of plastic wrap on a flat surface. Next, place a sheet of nori, shiny side down, rough side facing up, on top of the plastic wrap.
In the center of the nori, add a layer of sushi rice, approximately 1/3 cup, pressing it down and shaping it into a square at a 45-degree angle or diamond shape using slightly wet hands.
Layer on the tofu, mushrooms, cucumber, carrots, avocado, spicy mayo, sesame seeds, and another layer of rice, about 1/3 cup, pressing down gently to compact the ingredients.
Take a second piece of nori and cut it into a square that matches the size of your fillings. Place it on top of the rice and fold the sides of the nori over the filling. Firmly wrap the entire sushi sandwich with plastic wrap and gently squeeze it to seal everything together.
Allow the onigirazu to rest for 5 minutes to allow the flavours to meld together. Then, unwrap and cut it in half. Serve with spicy mayo or soy sauce for dipping, if desired.