Beat the eggs in a bowl with salt and pepper.
Heat butter or oil in a non-stick pan over medium heat. Add onions if using, cook until translucent before adding bell peppers for about 2 minutes more. Pour beaten eggs into the skillet spreading them out evenly to cover the bottom of the dish.
Let it sit undisturbed until edges start solidifying (about one minute). Once set around a quarter inch from edge, sprinkle cheese over half of omelette and fold with spatula. Cook an additional 30 seconds for golden brown crispy bottom - optional.
Slide the finished omelette onto plate
garnish as desired.