Preheat oven to 400 degrees. Cut chicken into 2-inch pieces. Spread panko on a rimmed baking sheet and bake until golden brown, 6 to 8 minutes. Transfer to a shallow dish, then add Parmesan and 1/2 teaspoon salt; drizzle with oil and stir to combine.
Place flour and eggs in separate shallow dishes. Increase temperature to 450 degrees.
Set a wire rack in a rimmed baking sheet; lightly coat rack with cooking spray. In batches, coat chicken in flour, shaking off excess, dip in egg, then coat with panko, pressing to adhere. Place on rack.
Bake until chicken is cooked through, 12 minutes, flipping halfway through. Serve nuggets with sauce
