In a small saucepan over medium heat, cook the eggs with the butter, stirring constantly, until the eggs are slightly runny, about 3 minutes Take them off the heat and season with salt and pepper. The residual heat will cook them through. Fold in half of the cheese and the chopped peppers.
To build the burritos, microwave the tortillas to soften. Divide the mixture among the center of the tortillas and top with the remaining cheese. Fold up the bottom third of the tortillas, fold the ends in towards the center and continue rolling to a small cylinder shape. Serve immediately.