Peel shrimp, and devein, if desired.
Combine shrimp, 1 tablespoon cornstarch, garlic, red pepper, 1 tablespoon soy sauce, and 1 tablespoon oil; let stand 5 minutes.
Whisk together remaining 2 tablespoons cornstarch, remaining 2 tablespoons soy sauce, chicken broth, and ginger; set aside.
Heat remaining 2 tablespoons oil in a large skillet or wok over medium-high heat 2 minutes. Add bell pepper strips, and stir-fry 4 minutes or until tender. Add green onions; stir-fry 2 minutes. Remove from skillet.
Add shrimp mixture to skillet; stir-fry 3 minutes. Reduce heat to low; add vegetables and chicken broth mixture, and stir-fry 3 minutes or until thickened and bubbly. Serve over hot cooked noodles.