Preheat the oven to 390°F (200°C). Lightly spray a baking sheet with oil and spread the panko breadcrumbs in an even layer; mix gently by hand. Bake the panko for 5–7 minutes until golden, then remove and increase the oven temperature to 430°F (220°C).
In a shallow bowl, break the egg and whisk briefly. Add the flour, mayonnaise, Dijon mustard, salt, and black pepper, stirring until you have a thick batter-like paste.
Place a chicken breast between two sheets of baking paper or cling film and gently flatten with a rolling pin or meat mallet until about 1/2 inch (1.25 cm) thick; repeat for all four breasts.
Set a wire rack over a baking sheet and lightly spray or brush with oil. Dip each flattened chicken breast into the batter, coating both sides, then press into the toasted panko so both sides are well covered. Transfer the coated breasts to the oiled rack.
Lightly spray the top of each coated chicken breast with oil, then bake on the rack at 430°F (220°C) for about 10 minutes, or until the crust is crispy and the chicken is cooked through.