In a small bowl, whisk together egg, salt, and pepper; set aside. Lightly coat an 8-inch nonstick skillet with flared sides with nonstick cooking spray. Preheat skillet over medium heat. Add mushrooms and onion to hot skillet; cook and stir until onion is tender. Remove vegetables from skillet; set aside.
Add 1 teaspoon of the oil to skillet; heat over medium heat. Add half of the egg mixture to skillet and immediately begin stirring gently with a wooden or plastic spatula. Stir continuosly until the mixture resembles small pieces of cooked egg surrounded by liquid egg. Stop stirring and cook for 30 to 60 seconds more or until egg mixture is set and shiny.
Spoon half of the mushroom mixture across one side of the cooked egg mixture. Top with 1 cup of the spinach and 1 tablespoon of the feta cheese. Loosen omelet edge from skillet. Fold unfilled side over the filling. Cook about 1 minute more or just until spinach starts to wilt. Slide omelet onto serving plate; cover and keep warm. Repeat to make a second omelet.
To serve, sprinkle omelets with the remaining 2 tablespoons feta cheese.