Heat olive oil in a large skillet over medium heat. Cook the potatoes 10-15 minutes or until golden brown. Remove and set aside.
In the same skillet cook onions and bell pepper until slightly softened, about 3 minutes. Add crumbled sausage. Cook until sausage is cooked through. Return the potatoes to the skillet.
Beat eggs and milk together in a bowl. Pour eggs over mixture. Cook for 2 minutes or until the edges of the eggs start to cook. Stir and cook until the eggs are cooked through. Add salt and pepper to taste. Sprinkle with cheddar cheese. Serve hot.