Whisk first 5 ingredients in medium bowl to blend. Add tofu and stir to coat; let marinate 30 minutes. Drain, reserving marinade in small bowl. Whisk 1/4 cup water and cornstarch into marinade.
Heat 1 tablespoon vegetable oil in large nonstick skillet over medium-high heat. Add tofu and sauté until golden, about 2 minutes. Using slotted spoon, transfer tofu to plate.
Add remaining 1 tablespoon vegetable oil to skillet. Add mushrooms and stir-fry until tender, about 3 minutes. Add sugar snap peas; stir-fry 2 minutes. Add garlic and ginger; stir-fry 30 seconds. Return tofu to skillet; drizzle reserved marinade mixture over. Stir-fry until marinade thickens slightly, about 30 seconds. Season to taste with salt and pepper. Transfer to bowl. Sprinkle with green onions and serve.