Preheat the air fryer to 400°F for 3-5 minutes. Slice all vegetables into ¼-inch thick rounds or planks using a sharp knife to ensure even cooking.
Pat the vegetable slices dry thoroughly with paper towels for 1-2 minutes to prevent soggy coating. Set up three shallow bowls: one with all-purpose flour, one with beaten eggs, and one with panko breadcrumbs.
Coat each vegetable slice first in flour, shaking off any excess. Dip into the egg wash until fully coated, then press into the panko breadcrumbs to cover both sides. Place the breaded pieces on a clean plate as you finish coating the batch.
Arrange the breaded vegetable slices in a single layer inside the air fryer basket, leaving about 1 inch of space between pieces to prevent steaming. Lightly spray the tops with vegetable oil spray. Air fry for 7 minutes at 400°F.
Flip the katsu pieces using tongs, spray the other side lightly with vegetable oil spray, and air fry for an additional 3 to 8 minutes, checking for a golden-brown crust and tender interior by piercing with a fork.
Serve immediately with katsu sauce on the side to keep the coating crispy.