In a non-stick skillet over medium-high heat, cook the pork sausage while breaking it into small crumbles until browned and fully cooked. Drain excess grease and set aside.
In a medium mixing bowl, whisk together eggs, milk, salt, and pepper until uniform in color.
Melt butter in a clean non-stick skillet over medium-low heat. Add the egg mixture and cook, stirring frequently with a spatula, until the eggs are just set and soft.
Warm the tortillas in the microwave for 20 seconds or on a dry skillet until pliable.
Lay a tortilla flat and place a portion of scrambled eggs, sausage crumbles, and shredded cheese in the center.
Fold the sides of the tortilla slightly inward and roll tightly from the bottom to create a wrap.
Place the roll-ups seam-side down in a hot skillet for 30 seconds per side to seal and melt the cheese further.
Serve immediately while warm.