Preheat an air fryer to 350 degrees F (175 degrees C).
Combine panko and Parmesan cheese on a plate. Dip 1 zucchini slice into beaten egg then into panko mixture, pressing to coat. Place zucchini slice on a wire baking rack and repeat with remaining slices. Lightly spray zucchini slices with cooking spray.
Arrange zucchini slices in a single layer in the air fryer basket, working in batches if necessary.
Cook in the preheated air fryer for 10 minutes; flip the slices and cook 2 minutes more. Repeat with remaining zucchini slices.