Heat a non-stick pan or skillet over medium heat. Once hot, add the oil. Brown the sausage on all sides.
Add the butter, eggs, tomatoes, scallions, and cheese into the pan. Move the eggs using circular motions with a spatula or wooden spoon to fluff up and cook, (move the pan on and off the heat as needed to prevent the eggs from overcooking or drying out). Remove the pan from the heat while the eggs are still moist. Season with pepper. Taste and add salt if needed.
Place the eggs on the wrap. Fold in the ends and roll up tightly.
(Place the wraps seam side down in the same nonstick pan over medium heat and cook to golden brown on both sides if desired).