Cook the udon noodles according to package directions. Drain and set aside.
In a large bowl, combine 2 tablespoons soy sauce, vinegar, and 2 teaspoons arrowroot.
Mix well, add the tofu, and mix gently. Let stand for 15 minutes. Preheat oven to 375 F.
In a measuring cup, combine the remaining 1 tablespoon soy sauce, 1 tablespoon arrowroot, 1/2 cup broth, hoisin sauce, and chili puree. Mix well and set aside.
Place tofu on a baking sheet. Bake until light brown, about 30 minutes, turning once. Remove tofu and set aside
Heat 1/4 cup broth in the wok. Add the ginger and garlic and stir-fry for 30 seconds.
Add the bell pepper, celery, and broccoli. Stir-fry for 1 minute. Pour in the remaining 1/4 cup broth, cover, and steam vegetables for 2 to 3 minutes
Add the sugar snap peas, cover, and steam for 1 to 2 minutes. Add the tofu and stir-fry for 1 minute.
Pour in the sauce and turn to coat the tofu and vegetables. Add the cooked udon noodles and turn to cover the noodles with sauce.