Heat 1/2 teaspoon of the oil in large nonstick skillet over medium heat until hot. Add mushrooms, onion, bell pepper and garlic; cook and stir 2 to 3 minutes or until onion and bell pepper are crisp-tender. Add turkey and basil; cook 1 to 2 minutes or until hot. Remove from skillet; set aside.
In small bowl, combine egg product, salt and pepper; blend well. Heat remaining 1/2 teaspoon oil in same skillet over medium heat until hot. Pour egg mixture into skillet. Cook until egg mixture is set, lifting edges occasionally to allow uncooked egg mixture to flow to bottom of skillet.
Spoon turkey-vegetable mixture over half of omelet; loosen edge of omelet and fold other half over filling.