Heat a large skillet over medium heat. Add the breakfast sausage and cook, breaking it into small crumbles, until no pink remains and it reaches 160°F (71°C). Transfer the sausage to a plate, leaving a little fat in the skillet; drain excess fat if needed.

Add the oil and cooked potatoes to the skillet. Cook, stirring occasionally, until hot and crisp at the edges, about 4 to 5 minutes. Add the bell pepper and onion; cook until softened, 3 to 4 minutes.

Whisk the eggs with the optional milk, salt, and pepper. Lower the heat to medium-low, pour the eggs into the pan, and gently stir until softly set. Return the sausage and fold it through the eggs and vegetables.

Warm the tortillas briefly so they bend without cracking. Divide the filling among them, top with cheddar, fold the sides inward, and roll tightly. For crisp burritos, place them seam-side down in the skillet for 1 to 2 minutes per side.