In a medium bowl, whisk together the eggs, whole milk, salt, and black pepper until well combined.
Heat a large non-stick skillet over medium heat. Add the breakfast sausage and cook, breaking it up with a spatula, until browned and cooked through, about 5-6 minutes. Remove the cooked sausage from the skillet and set aside.
In the same skillet, pour in the egg mixture. Cook over medium-low heat, stirring gently with a spatula, 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 for about 15 seconds to make them pliable.
Divide the scrambled eggs evenly among the tortillas, placing the eggs in the center of each tortilla.
Top the eggs with the cooked sausage and then sprinkle evenly with shredded cheddar cheese.
Roll up each tortilla tightly around the filling, folding in the sides as you roll to create a secure roll-up.
Place the roll-ups seam side down on a clean skillet over medium heat. Cook for 1-2 minutes on each side, or until the tortillas are golden brown and the cheese is melted.
Remove from heat, slice in half if desired, and serve immediately.