Preheat the oven to 200 degrees F (95 degrees C).

Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes. Transfer sausage to a bowl and set aside. Add oil to the skillet and heat over medium heat. Add bell pepper and onion; season with salt and pepper and cook until softened, 3 to 5 minutes. Transfer to a bowl.

Add sweet potatoes to the hot skillet. Season with salt and black pepper; cook and stir frequently for 5 minutes. Cover skillet and cook 5 minutes more. Remove lid and cook until potatoes are browned, stirring frequently, 5 to 7 minutes more. Set aside.

Whisk eggs, milk, 1/2 cup Cheddar cheese, garlic powder, dry mustard, salt, and black pepper together in a bowl.

Heat a nonstick pan over medium heat. Add egg mixture and scramble until nearly done but still a bit wet, about 5 minutes. Remove from heat.

Layer sweet potatoes in the bottom of a 9x13-inch baking pan. Pour in scrambled eggs, 1/2 cup Cheddar cheese, onion-pepper mixture, and sausage, in that order. Top with remaining cheese.

Bake in the preheated oven until warmed through, about 10 minutes or until ready to serve.