Press the cubed tofu: wrap tofu in a clean towel or paper towels on a cutting board, place a heavy weight on top, and let sit 15 minutes to remove excess water.
Make the sauce: in a medium bowl whisk together tamari, 1/2 cup water, maple syrup, minced garlic, chopped ginger, honey or extra maple syrup, and rice vinegar until combined.
Marinate the tofu: place pressed cubed tofu in a container, pour about one third of the sauce over it, seal, and shake to coat; refrigerate 15 minutes to overnight (optimal at least 1 hour).
Preheat the oven to 400°F (200°C) and line a sheet pan with parchment paper.
Soak the rice noodles in very hot tap water for 30 minutes, then drain and set aside. When ready to finish, briefly boil the noodles 1 minute in a large pot of boiling water, drain, rinse in cold water, and separate with tongs.
Heat the remaining sauce in a small saucepan over medium-high heat until bubbling. In a small bowl stir together 1 tablespoon cornstarch and 2 tablespoons cold water, then whisk the slurry into the bubbling sauce and cook until thickened. Remove from heat and set aside.
Arrange the marinated tofu on the prepared sheet pan; bake 15 minutes, then flip the tofu and add broccoli, mushrooms, and sliced onion to the pan. Drizzle a few tablespoons of the thickened sauce over the vegetables and bake 8 more minutes.
Add snow peas to the sheet pan and bake an additional 5–8 minutes, until vegetables are tender-crisp and tofu is browned at the edges.
Combine: place cooked noodles in a large serving bowl, add baked tofu and vegetables, pour remaining sauce over everything, and gently toss to combine.
Serve: divide into bowls and garnish with toasted sesame seeds and sliced green onions.