In a deep, wide dish or pie plate, combine the soy sauce, honey, garlic and ginger. Add the tofu and let it marinate for at least an hour, turning it over half way through.
Cook the rice according to the package. In a large glass or ceramic bowl, combine the rice vinegar and sugar. Add the hot rice in fourths, stirring the mixture well after each addition. Stir in the scallions and sesame seeds, mix well.
For each roll, place a sheet of nori on a piece of wax paper so that the bottom edge of the nori lies along the bottom edge of the paper. Moisten your hands with cold water and place a handful of rice in the center of the nori, spread it out in a thin layer to fill the sheet evenly. Add more rice if necessary. Place 2 strips of tofu across the center of the nori, so they run the entire width of the sheet. Place a portion of the carrots on top of the tofu, some spinach over that, finishing with some sprouts (use about a fifth of each filling ingredient). Start rolling the nori from the bottom by gripping the nori and the wax paper, and using the paper to help you make a tight roll.
Let the nori rest, seam side down, while you repeat the remaining procedure with the remaining rice and nori. You should have 5 rolls. To serve, wet the blade of a serrated knife and cut rolls into rounds about an inch thick. Serve at room temperature.