Crack the eggs into a bowl. Whisk with salt and pepper until smooth.
Heat butter in a non-stick skillet over medium heat. Pour in the eggs and cook, stirring occasionally, until scrambled and just set.
Warm the tortillas in a skillet or microwave until soft and pliable.
Place scrambled eggs in the center of each tortilla. Sprinkle cheese on top while the eggs are hot.
Add any optional toppings like hot sauce or cooked meat. Fold the sides, roll up the burrito tightly, and toast in a skillet seam-side down if desired.