Preheat oven to 350°F (175°C). Grease a 9x13 inch baking dish and set aside.

Heat a large skillet over medium heat and add 1 lb of the breakfast sausage. Break it into small crumbles with a wooden spoon and cook for 6-8 minutes until no pink remains and the sausage develops crispy brown edges. Drain excess grease, leaving about 1 tablespoon in the pan.

While the sausage browns, melt 1 tablespoon butter in a separate pan over medium-low heat. Pour in beaten eggs and gently scramble until slightly soft and glossy. Remove from heat.

Cook hash browns or tater tots according to package directions until golden and crispy, about 8-10 minutes if frozen. Pat thoroughly dry with paper towels.

In a large bowl, combine cooked sausage, scrambled eggs, crispy potatoes, and 1 cup shredded cheddar cheese. Mix gently but thoroughly.

If tortillas are cold, warm them in the microwave for 15-20 seconds wrapped in a damp paper towel. Divide filling evenly among the six tortillas, spooning it in a line down the center, leaving about an inch on each end. Roll each tortilla tightly and place seam-side down in the greased baking dish, packing them snugly together.

For the gravy, melt 2 tablespoons butter in a medium saucepan over medium heat. Add the remaining 0.5 lb sausage and cook until browned and crumbly, about 5-6 minutes. Sprinkle flour directly over the sausage and butter, stirring continuously for 2 minutes to create a golden roux.

Slowly pour in cold milk in a thin stream while whisking constantly. Continue whisking until gravy thickens enough to coat the back of a wooden spoon, about 7-10 minutes. Season generously with salt and freshly cracked black pepper.

Pour warm sausage gravy evenly over all rolled enchiladas, ensuring each one is well-covered. Sprinkle remaining 0.5 cup cheddar cheese on top.

Bake uncovered at 350°F for 20-25 minutes until cheese melts and turns golden at the edges, with bubbling around the sides. Let rest 5 minutes before serving.