To prepare sauce, combine first 10 ingredients, stirring well with a whisk.
Heat 1 tablespoon canola oil in a large nonstick skillet over medium-high heat. Add tofu; cook 8 minutes or until lightly browned, turning occasionally. Remove from pan. Add the remaining 1 1/2 teaspoons canola oil, button mushrooms, and shiitake mushrooms to pan; sauté 3 minutes or until almost tender. Add peas, bell pepper, and water chestnuts; sauté 1 minute. Stir in broth mixture, tofu, oyster mushrooms, and onions; cook 2 minutes or until slightly thick. Serve over rice.