Prepare the veggies: Heat a nonstick skillet over medium heat and add butter or olive oil. Sauté the diced onion and bell pepper for 3–4 minutes until softened and fragrant, stirring occasionally to avoid burning.
Cook the eggs: In a bowl, whisk together eggs, milk, salt, and pepper until smooth. Pour the mixture into the skillet with the veggies. Stir gently as it cooks, folding the eggs over themselves until soft, fluffy, and just set, about 3–4 minutes.
Add chicken and cheese: Stir in the cooked chicken and half of the shredded cheese. Continue cooking for another 1–2 minutes until the chicken is warmed through and the cheese begins to melt.
Assemble the wrap: Warm the tortillas in a separate dry skillet or microwave for 10–15 seconds to make them pliable. Spoon the egg and chicken mixture evenly onto each tortilla. Sprinkle the remaining cheese on top.
Wrap it up: Fold the sides over the filling and roll the tortilla tightly into a wrap. For a crispier finish, place the wrap seam-side down in a lightly oiled skillet for 1–2 minutes on each side until golden brown.
Serve: Slice the wraps in half diagonally and serve immediately. Add optional toppings like avocado slices, hot sauce, or fresh herbs for extra flavor and a beautiful presentation.