Cut a square of plastic wrap slightly larger than a nori sheet. Place the plastic wrap on the kitchen counter and place a nori sheet on top, shiny-side down, at a 45-degree angle to the plastic wrap, so it looks like a diamond shape on a square.
Keep a small bowl of water to the side. Wet hands in the water bowl and place a large handful of rice in the center of the nori sheet. Using your hands, form the rice into an approximate 3 1/2-inch square. Season well with salt and repeat the process with the remaining nori sheets.
Top the rice with avocado. For the tofu sandwich, place the tofu, carrot and cucumber on top of the avocado. Repeat to make 1 more tofu sandwich. For the spinach sandwich, place spinach, pickled red cabbage and red pepper on top of the avocado. Repeat to make 1 more spinach sandwich. Sprinkle 1/2 teaspoon black sesame seeds over the filling in each sandwich.
To close the sandwiches, seal all four corners of the nori over the ingredients. Fold the right corner over the stack and dampen the folded-over corner using wet fingers. Fold the left corner on top of the damp right corner and press to seal the two corners together. Repeat with the top and bottom corners to seal the sandwich completely.
To set your sandwiches, gather the plastic wrap over the sandwiches and place something heavy like a cutting board or a book on top of each. Allow each sandwich to sit for 5 to 10 minutes before unwrapping.