In large saucepan, bring 4 quarts salted water to a boil. Add green beans and boil 4 minutes. Add carrots and boil 1 minute longer. Drain well.
In small bowl, combine chicken broth, soy sauce, hoisin sauce, and cornstarch. Set aside.
In large nonstick skillet, heat oil over high heat. Add tofu and stir-fry until golden brown, about 3 minutes. Add mushrooms, garlic, and ginger; cook 3 minutes. Stir broth mixture to blend well, add to skillet, and cook 1 minute. Stir in green beans and carrots, and toss to coat.