In a large skillet, cook the breakfast sausage over medium heat until browned and fully cooked, breaking it apart with a spoon as it cooks. Once cooked, drain any excess grease and set the sausage aside.
Scramble the Eggs:
In a bowl, whisk the eggs and milk together until well combined. Season with a pinch of salt and pepper.
In the same skillet (or a separate one), melt the butter over medium-low heat. Pour in the egg mixture and scramble gently, stirring occasionally until the eggs are just set but still soft. Remove from heat and set aside.
Assemble the Roll-Ups:
Lay out the tortillas on a flat surface. Evenly distribute the cooked sausage and scrambled eggs among the tortillas, placing them in the center of each tortilla.
Sprinkle a generous amount of shredded cheese over the sausage and eggs.
Roll Them Up:
Carefully fold in the sides of each tortilla and then roll it up tightly, encasing the filling inside.
Optional: Warm the Roll-Ups:
For a warm and slightly crispy exterior, you can heat the roll-ups in a skillet. Place the roll-ups seam-side down in a heated skillet over medium heat and cook for 2-3 minutes on each side until the tortillas are golden brown and the cheese inside has melted.
Serve:
Serve the roll-ups as is, or with a side of hot sauce or salsa for dipping.