Heat a non-stick pan over medium heat. Once hot, add the oil. Saute the sausage until golden brown. Add in the butter, onions, and peppers. Saute until softened.
Pour in the eggs and reduce the heat to medium-low. Use a spatula to stir the eggs around the pan until the eggs are set. Season with salt and pepper to taste.
Place the wrap on a baking sheet. Spread the cheese onto the wrap. Place under the broiler until the cheese is melted, about 1 to 2 minutes. Then set aside.
Portion the eggs onto the wrap. Fold in the ends and roll up tightly.