Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Trim and cut the chicken breasts into bite-sized cubes, then season with the salt and ground 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 cube in the flour, shaking off excess, then dip into the egg, and finally press into the cooked quinoa so it adheres to the surface.
Place the coated nuggets side by side on the prepared baking sheet and lightly drizzle them with the olive oil.
Bake for 40 to 45 minutes, or until the nuggets are golden brown and cooked through (internal temperature 165°F / 74°C).
Remove from the oven and serve hot with your favorite sauce.