Whisk the eggs in a small bowl.
Pour half the eggs into a nonstick pan over medium heat. Immediately place a tortilla on top of the wet egg and press down gently.
Cook 5 minutes, until the egg is set and bonded to the tortilla. Slide onto a cutting board, egg side up.
Cut one straight line from the center of the tortilla to the bottom edge, stopping at the center.
Spread mayonnaise on the lower left quarter.
Add chopped lettuce to the upper left quarter.
Add tomato slices to the upper right quarter.
Add cheese to the lower right quarter.
Starting with the mayonnaise quarter, fold it up over the lettuce. Fold that stack over the tomato. Fold down over the cheese to form a triangle.
Spray the air fryer basket with cooking spray or line with parchment.
Place the wrap fold-side down and spray the top lightly with oil.
Air fry at 400°F for 3 minutes per side, flipping once, until golden and crisp.
Rest 1 minute before serving. Repeat with the remaining tortilla and eggs.