Place the breakfast sausage in a large skillet over medium-high heat. Break it apart with a spatula and cook until browned and cooked through, about 5-7 minutes. Remove the sausage and set it aside, draining all but one tablespoon of grease.

In a mixing bowl, crack the eggs. Add the milk, salt, and pepper. Whisk vigorously until the mixture is pale yellow and slightly frothy.

Melt the butter in the skillet with the reserved sausage grease over medium heat. Pour in the egg mixture. Let sit for 20-30 seconds until the edges begin to set. Gently push the eggs from the edges toward the center until soft, slightly moist curds have formed.

Return the cooked sausage to the skillet with the eggs. Sprinkle the shredded cheddar cheese over the top. Gently stir until the cheese is melted and combined.

Warm the tortillas in the microwave or a dry skillet. Spoon the egg and sausage mixture evenly into the warm tortillas. Add your favorite toppings and serve immediately.