3 large eggs
1 tablespoon butter
¼ cup diced smoked ham
2 tablespoons diced onion
2 tablespoons diced green bell pepper
salt and freshly ground black pepper to taste
⅓ cup shredded Cheddar cheese
1 pinch cayenne pepper
Beat eggs in a small bowl until just combined; do not overbeat.
Melt butter in a skillet over medium-high heat. Add ham, onion, and bell pepper; season with salt and pepper. Cook and stir until onions soften and ham begins to caramelize, about 5 minutes.
Reduce heat to medium-low and pour in eggs. Mix briefly with a spatula while shaking the pan to ensure ingredients are evenly distributed. Quickly run the spatula along edges of omelet. Sprinkle Cheddar cheese and cayenne pepper over omelet.