Denver Omelette with Ham, Peppers, and Onions

Dice the ham, bell pepper, and onion into roughly 1/4-inch pieces so they distribute evenly through the eggs.

Melt 1 tablespoon of butter in a 10-inch nonstick skillet over medium heat. Add the bell pepper and onion and cook, stirring occasionally, until softened and lightly golden, about 4 to 5 minutes. Stir in the ham and cook 1 minute more, just to warm it through. Transfer the mixture to a plate.

In a bowl, whisk the eggs with the milk, salt, and pepper until the yolks and whites are fully combined and the mixture looks uniform, about 30 seconds.

Wipe the skillet clean and return it to medium-low heat. Melt 1/2 tablespoon of butter, swirling to coat the pan. Pour in half the egg mixture and let it set undisturbed for about 1 minute, then use a spatula to gently push the cooked edges toward the center, tilting the pan so raw egg runs to the edges. Cook until the top is just barely set, about 1 to 2 minutes.

Scatter half the ham mixture and half the cheddar over one side of the omelette. Fold the other half over the filling and slide the omelette onto a plate. Repeat with the remaining butter, eggs, and filling to make the second omelette.

Serve immediately while the cheese is melted and the eggs are still tender. Garnish with extra black pepper if you like.