Start by preparing the pickles (can be made a few days ahead): Heat the water, sugar, and salt in a saucepan over medium heat to dissolve the sugar. Once dissolved, transfer to a bowl or jar. Add the vinegar, carrots, and radish. Refrigerate for at least 1 hour or up to 7 days.
Cut the tofu into thin slices and transfer to a deep plate. In a small bowl, prepare the marinade by combining the soy sauce, maple syrup, lime juice, garlic, and five-spice if using. Pour the marinade over the tofu and make sure each tofu slice is covered with the marinade. Let marinate for at least 30 minutes or up to 1 day in the refrigerator.
Heat a teaspoon of oil in a non-stick skillet. Once hot, add the sliced mushrooms and cook for about 5 minutes, or until mushrooms are cooked. Deglaze with a teaspoon of soy sauce and cook for another 30 seconds. Transfer the mushrooms to a small bowl.
To the same skillet, add the tofu with the marinade and cook for about 5 minutes, or until almost no liquid remains. Remove from heat.
To assemble: cut the sesame donuts in half. Spread about 2 tbsp of hummus on the inside. Add a leave of lettuce, avocado, some sautéed mushrooms, a few slices of red onion, some carrots and radish, and finally a couple of slices of teriyaki tofu. Repeat with the remaining donuts and serve immediately at room temperature!