Wrap the flour tortillas in paper towels and microwave them for 1 minute to make them pliable. Set them aside.
Crumble the sausage finely into a large skillet over a medium heat and cook until brown, 5 to 6 minutes.
Add the butter to a large nonstick skillet over a medium heat. Beat the eggs in a large bowl with the salt and pepper. When the butter has melted, turn the heat to low and pour in the eggs, then the sausage. Slowly cook the mixture, using a wooden spatula to push it around the skillet, until the eggs are totally cooked through, 8 to 10 minutes.
Place approximately 1/2 cup of the egg and sausage mixture into a warm tortilla, along with a pinch of cheese. Roll up (do not tuck in the ends). Wrap in a foil square and keep warm until ready to serve. Repeat with the remaining ingredients.