Preheat your oven: Set your oven to 375°F (190°C).
Whisk the eggs: In a bowl, whisk together eggs, milk, salt, and pepper until frothy. Set aside.
Sauté the veggies: Heat butter or oil in a cast iron skillet over medium heat. Add onion and peppers; cook for 3–4 minutes until softened.
Add ham: Stir in diced ham and cook for another 2 minutes to warm through.
Add the eggs: Pour the egg mixture over the veggies and ham. Let it cook for 2–3 minutes until the edges begin to set.
Top with cheese and bake: Sprinkle cheddar on top, then transfer skillet to the oven. Bake for 12–15 minutes, or until the center is set.
Cool and serve: Let rest 5 minutes before slicing. Serve warm or at room temperature.