Preheat the oven to 400°F (200°C) and line a baking sheet with parchment or use a nonstick sheet.
Place the chicken cubes in a large mixing bowl and add the lightly whipped egg white; toss to evenly coat the chicken.
Add black pepper, cayenne, onion powder, and salt to the coated chicken and mix to distribute the seasonings.
Add the whole wheat panko breadcrumbs and toss or press them onto the chicken pieces so they are well coated.
Arrange the coated chicken pieces in a single layer on the prepared baking sheet, leaving a little space between pieces.
Drizzle the tablespoon of oil over the nuggets or lightly spray with oil, then bake for 30 minutes until golden and cooked through.
Check one piece for doneness (no pink inside); remove from oven and serve.