In a medium bowl, whisk together the eggs, whole milk, salt, and black pepper until well combined.
In a large skillet over medium heat, cook the breakfast sausage, breaking it apart with a spatula, until browned and fully cooked, about 7-8 minutes. Remove the sausage from the skillet and set aside.
In the same skillet, melt the butter over medium heat. Pour in the egg mixture and cook, stirring gently, until the eggs are softly scrambled and just set, about 3-4 minutes. Remove from heat.
Warm the flour tortillas in a dry skillet or microwave until pliable, about 20 seconds in the microwave.
To assemble each roll-up, evenly distribute the scrambled eggs down the center of each tortilla. Top with cooked sausage and sprinkle with shredded cheddar cheese.
Fold the sides of the tortilla over the filling and then roll tightly from one end to the other to form a roll-up.
Optional: Place the roll-ups seam side down in a clean skillet over medium heat and cook for 1-2 minutes on each side until the tortillas are golden and the cheese is melted.
Serve warm and enjoy your Sausage Egg Breakfast Roll-Ups!