Heat your oven to 400°F first. Cut the chicken breasts into bite-size pieces, roughly the same size. Even pieces cook at the same speed, so none dry out.
Spread the panko in a thin layer on a rimmed baking sheet. Bake it for about 5 minutes until lightly golden. This step gives the nuggets a deep, toasty flavor and a rich color.
Move the toasted panko into a shallow dish. Stir in the Parmesan, salt, and pepper. Drizzle in the oil and toss well so every crumb is lightly coated.
Put the flour in one dish and the beaten eggs in another. Keep the panko mix in the third. Line them up in order so you can work fast and keep your hands tidy.
Raise the oven temperature to 450°F. Set a wire rack on the baking sheet and spray it lightly with cooking spray. This keeps the nuggets from sticking and helps the bottoms crisp up.
Work in small batches. Roll each piece in flour and shake off the extra. Dip it in egg, then press it firmly into the panko mix until fully covered.
Place the nuggets on the rack with a little space between them. Bake for 12 to 15 minutes. Flip them halfway through so both sides turn crunchy and golden.
Let the nuggets sit for a couple of minutes after baking. The coating firms up as it cools slightly. Serve them warm with your favorite dip.