In a medium bowl, whisk together the eggs, whole milk, salt, and black pepper until fully combined.
Heat a large non-stick skillet over medium heat. Add the breakfast sausage and cook, breaking it apart with a spatula, until browned and cooked through, about 6-8 minutes. Remove the sausage from the skillet and set aside.
In the same skillet, melt the unsalted 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.
Return the cooked sausage to the skillet with the scrambled eggs and stir to combine evenly.
Warm the flour tortillas in a dry skillet or microwave for 10-15 seconds to make them pliable.
Divide the sausage and egg mixture evenly among the tortillas, placing it in the center of each. Sprinkle 1/4 cup shredded cheddar cheese over the filling on each tortilla.
Roll up each tortilla tightly, folding in the sides as you roll to create a neat roll-up.
Optional: Place the roll-ups seam-side down in a clean skillet over medium heat for 1-2 minutes per side to lightly toast and melt the cheese inside.
Serve warm and enjoy your Sausage Egg Breakfast Roll-Ups!