Preheat oven to 300 degrees F. In a small bowl, beat together eggs, salt, and pepper. Coat an unheated 8-inch nonstick skillet with cooking spray. Heat over medium heat. Pour 1/2 cup of the egg mixture into the hot skillet.
Using a large spoon or spatula, immediately begin stirring gently but continuously until mixture resembles small pieces of cooked egg surrounded by liquid egg. Stop stirring. Cook for 30 to 60 seconds more or until egg mixture is set but still glossy.
Sprinkle 1/8 teaspoon of the dried oregano onto omelet. Place 4 slices of tomato on top of half of the omelet.
With a spatula, lift and fold opposite edge of the omelet over tomato slices. Transfer to a baking sheet; keep warm in oven. Sprinkle with 1/4 cup cheese. Repeat with remaining egg mixture, oregano, tomato, and cheese to make three more omelets.