Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking dish.
Scramble the eggs in a large skillet over medium heat for about 5 minutes until just set.
Stir in the cooked beef sausage, hash browns, and shredded cheese until the cheese begins to melt.
Spoon the filling into each tortilla and roll tightly.
Arrange the rolled tortillas seam-side down in the prepared baking dish.
For the gravy, brown the remaining beef sausage in a medium saucepan.
Sprinkle in the flour and stir for about 1 minute.
Slowly whisk in the milk until smooth.
Simmer for 5–7 minutes until the gravy thickens.
Season with salt and pepper.
Pour the gravy evenly over the enchiladas.
Cover with foil and bake for 25 minutes.
Remove the foil and continue baking for 10 minutes until bubbly and lightly golden.
Let the Breakfast Enchiladas with Sausage Gravy rest for 5 minutes before serving.
Garnish with fresh parsley or extra shredded cheese if desired.