Combine ginger and 1/2 teaspoon salt in a small bowl; let stand for 5 minutes. Rinse ginger with cold water; pat dry. Combine ginger and cornstarch in bowl.
Heat oil in a wok or large nonstick skillet over medium-high heat. Add mushrooms, and stir-fry 2 minutes or until tender. Add the ginger mixture, snow peas, and chile, and stir-fry 2 minutes. Add tofu; stir-fry 1 minute. Add onions and soy sauce; stir-fry 2 minutes.