Preheat the oven to 425°F (220°C). Brush a metal baking sheet with 1 tablespoon olive oil and set it aside.
Season the chicken pieces with the kosher salt and black pepper; set aside.
In a shallow dish, combine the panko, grated Parmesan, dried oregano, and garlic powder; mix to combine.
Place the flour in a second shallow dish and beat the egg in a third shallow dish.
Working one piece at a time, dredge a chicken piece in the flour, shaking off excess, then dip it in the beaten egg, allowing excess to drip off, and finally coat it in the panko-Parmesan mixture. Place the coated piece on the oiled baking sheet.
Repeat until all chicken pieces are coated and arranged in a single layer on the baking sheet without crowding.
Bake for 7 minutes, remove the sheet and flip each nugget, then return to the oven and bake another 7–8 minutes, until the chicken is cooked through and the coating is golden.
Remove from oven and let rest for a minute before serving.