Heat 1/2 teaspoon oil in a large nonstick skillet coated with cooking spray over medium-high heat until hot. Add beef; stir-fry 2 minutes. Remove beef from skillet; set aside. Wipe skillet clean with a paper towel.
Heat 1/2 teaspoon oil in skillet. Add sliced shallots, bell pepper strips, and minced garlic, and stir-fry 1 minute. Add mushrooms, and stir-fry 2 minutes. Stir in wine, and cook 1 minute. Add broth; reduce heat, and simmer 3 minutes. Return beef to skillet, and cook 1 minute. Stir in chopped basil, salt, and pepper. Serve with rice.