Whisk the eggs in a large bowl. Season with salt and pepper to taste.
In a large skillet over medium heat, sauté the chopped red pepper and onion until softened, about 5 minutes.
Add the diced ham to the skillet and cook for an additional 2-3 minutes.
Pour the egg mixture into the skillet with the ham and vegetables. Stir gently to combine.
Cook the egg mixture, stirring occasionally, until the eggs are mostly set but still slightly runny, about 5-7 minutes.
Layer on egg, then cheese evenly on the 4 wraps.
Top each wrap with 2 tablespoons of salsa.
Roll up the wraps tightly, tucking in the sides as you go.
Toast each side in the same egg pan on medium heat. Until each side is golden brown and crispy.