Heat 1 tablespoon of your oil in your oven safe skillet. Stir in diced potatoes coating them with the oil. Cook for 10 minutes, stirring occasionally. Transfer to a dish and set aside.
Add another tablespoon of oil to your pan. Add sausage, onion, and peppers. Stir to coat with the oil and cook for about 3 minutes, stirring occasionally until the onions are translucent. Transfer to the dish with the potatoes.
Whisk eggs until they are foamy and well scrambled. Then stir in the previously sautéed ingredients and seasonings.
Now heat the remaining 2 tablespoons of oil plus 2 tablespoons of butter in your skillet and coat the bottom and sides.
Pour egg mixture into the hot pan, cover, and cook for 2 minutes.
Meanwhile preheat your broiler on low
Uncover your skillet and place the oven safe skillet under the broiler about 7 inches from the heat source, until the top is golden brown and fluffy, about 4 minutes.
Cut into slices and serve immediately.