Lay the flour tortillas out flat on a cutting board. In the center of each tortilla, spread two tablespoons refried beans. Next, add one-fourth cup eggs and two tablespoons cheese to each tortilla.
To fold the tortillas, begin on the left side and fold to the center. Then fold the right side into the center. Next, fold the bottom and top down and roll over to completely seal the chimichanga. Using a pastry brush or an oil mister, brush the tops of the tortilla packages with oil.
Preheat the air fryer to 400 degrees Fahrenheit. Place the chimichangas into the air-fryer basket seam side down, and air-fry for four minutes. Using tongs, turn over the chimichangas and cook for an additional two to three minutes or until light golden brown.
Serve with guacamole, salsa, and sour cream for a hearty breakfast. You can also vary it by swapping out beans with breakfast potatoes or rice. Serves four.