Cook the sausage. Heat a skillet (frying pan) over medium-high heat. Add the sausage and break it into small crumbles as it cooks. Cook until browned with no pink remaining, about 5–6 minutes. Add the diced roasted pepper and cook until warmed through, about 30 seconds. Transfer the sausage and pepper to a plate.
Make the scrambled eggs. Whisk the eggs with a pinch of salt until smooth. Add half the butter to the skillet (frying pan) over medium heat. Once the butter has melted, add the whisked eggs and stir gently until softly set but still slightly glossy, about 1–2 minutes. Remove the eggs and wipe the skillet clean.
Assemble the wrap. Warm up the tortilla for 10 seconds in the microwave so it doesn't tear. Sprinkle the cheese all over the tortilla, then add the cooked sausage, pepper, and eggs. Fold in the sides and roll up tightly.
Toast in the skillet. Return the skillet to medium heat. Add the remaining butter. Once the butter has melted, place the wrap seam-side down and toast until golden, about 1–2 minutes. Turn and toast the remaining sides until golden all over and the cheese is melted.
Serve.