Prepare the eggs: In a medium bowl, whisk together eggs, milk, salt, and pepper until smooth and slightly frothy. This ensures your scrambled eggs will be light and fluffy.
Cook the eggs: Heat butter or oil in a nonstick skillet over medium heat. Pour in the egg mixture and let it sit for a few seconds before gently stirring with a spatula. Continuously fold the eggs from the edges to the center until they are fully cooked but still soft and creamy. Avoid overcooking, as the eggs will continue to cook slightly even after removing from heat.
Warm the tortillas: While the eggs are cooking, warm the tortillas in a dry skillet for 30–60 seconds on each side or wrap in a damp paper towel and microwave for 20–30 seconds. This makes them pliable and easier to roll.
Assemble the wrap: Place a warm tortilla on a plate. Add half of the scrambled eggs to the center, sprinkle with shredded cheese, and layer any optional fillings you like. Fold in the sides of the tortilla and roll tightly into a wrap. Repeat for the second tortilla.
Optional finishing touch: For extra flavor and a lightly crisp exterior, place the wraps seam-side down in a skillet over medium heat for 1–2 minutes per side until golden brown.
Serve: Slice each wrap in half on a diagonal and serve immediately. Pair with fresh fruit, salsa, or hot sauce for a complete and satisfying breakfast.