Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Pat the chicken dry and cut into bite-size cubes; season evenly with the salt and pepper.
Set up three shallow bowls: one with the whole-wheat flour, one with the lightly whisked egg, and one with the cooked quinoa.
Dredge each chicken piece in flour, shaking off excess, then dip into the egg, letting excess drip off.
Press the egg-coated chicken into the cooked quinoa until the quinoa adheres, coating all sides.
Arrange the coated nuggets side by side on the prepared baking sheet and drizzle them with the olive oil.
Bake for 40–45 minutes, turning once halfway through if desired, until the nuggets are golden brown and cooked through.
Remove from the oven and serve hot with your favorite sauce.