Heat a large skillet over medium heat. Cook one pound of breakfast sausage until browned. Break it into small pieces while cooking. Drain excess grease and set the sausage aside for later use.

Melt butter in the same skillet. Beat the eggs with salt and pepper. Cook gently until soft and fluffy. Avoid overcooking because the eggs will continue cooking later in the oven.

Place the cooked eggs in a large bowl. Add the cooked sausage, green onions, and one cup of shredded cheese. Stir everything together until well mixed and evenly combined.

Lay each tortilla flat on a clean surface. Spoon the filling into the center of each tortilla. Roll tightly and place seam-side down in a greased baking dish.

Cook the remaining sausage in a saucepan. Stir in the flour and cook for one minute. Slowly whisk in the milk. Cook until thick and creamy. Add salt and pepper.

Pour the warm sausage gravy evenly over the rolled enchiladas. Sprinkle the remaining cheese across the top. Make sure every enchilada gets covered with gravy and cheese.

Bake in a preheated 375°F (190°C) oven for 25 to 30 minutes. The cheese should melt completely. The edges should become lightly golden and bubbly.

Remove the baking dish from the oven. Let it rest for five minutes before serving. This helps the filling set and makes serving much easier.