Snap off tough ends of asparagus. Cut spears diagonally into 2-inch pieces. Set aside.
Combine vegetable broth, soy sauce, and cornstarch in a small bowl; stir with a whisk until smooth. Set aside.
Heat 1 tablespoon sesame oil in a large nonstick skillet over medium-high heat. Add tempeh, and stir-fry 4 to 5 minutes or until golden. Remove tempeh from pan; set aside.
Heat remaining 1 tablespoon sesame oil in same pan. Add garlic, red pepper, asparagus, and mushrooms to pan, and stir-fry 3 minutes or until asparagus is crisp-tender. Add broth mixture; bring to a boil, and cook 2 to 3 minutes or until thickened. Add tempeh, and cook 1 minute or until thoroughly heated. Serve over brown rice.