In a small bowl, stir together eggs, salt and pepper. Coat an unheated 8-inch nonstick skillet with nonstick cooking spray. Preheat over medium heat. Pour ½ cup of the egg mixture into the hot skillet.
Immediately begin stirring egg mixture gently but continuously with a wooden or plastic spatula 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 shiny.
Sprinkle half of the oregano onto eggs. Place 2 slices of tomato on top of one half of the egg mixture in skillet. Top with half of the shredded mozzarella.
With a spatula, lift and fold opposite edge of the omelet over tomato slices. Transfer to a warm plate. Repeat with remaining egg mixture, oregano, tomato and cheese to make another omelet.