Preheat oven to 425°F (220°C). Brush a metal baking sheet with the 1 tablespoon olive oil and set aside.
Pat the 1 lb chicken pieces dry. Sprinkle them with 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper; set the chicken aside.
In a shallow dish, combine 1 cup panko breadcrumbs, 1/2 cup freshly grated Parmesan, 1 teaspoon dried oregano, 1/2 teaspoon garlic powder, the remaining 1/2 teaspoon kosher salt, and the remaining 1/4 teaspoon black pepper; mix well.
In a second shallow dish, whisk the 1 egg until blended.
Place the 1/4 cup flour in a third shallow dish.
Working one piece at a time, dredge a chicken piece in the flour and shake off excess.
Dip the floured piece in the beaten egg, letting excess egg drip off.
Press the egg-coated piece into the panko-Parmesan mixture to coat all sides, shaking off any loose crumbs. Place the coated piece on the prepared baking sheet in a single layer with space between pieces.
Repeat steps 6–8 until all chicken pieces are coated and arranged on the baking sheet.
Bake for 7 minutes. Remove the baking sheet, flip each nugget, and return to the oven. Bake an additional 7 minutes, or until the chicken is cooked through (internal temperature 165°F / 74°C) and the coating is golden.