In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add the finely chopped onion and sauté for about 5-7 minutes, or until the onion is translucent and fragrant.
In a large mixing bowl, combine the cooked quinoa, shredded chicken, black beans, diced green chiles, and enchilada sauce. Add the sautéed onion and mix everything together until well combined.
Spread half of the quinoa mixture evenly in the bottom of a greased 9x13 baking dish. Sprinkle half of the cheddar and mozzarella cheeses over the top. Add the remaining quinoa mixture, and top with the rest of the cheese.
Cover the baking dish with aluminum foil and bake in a preheated oven at 350°F (175°C) for 25 minutes. Remove the foil and bake for an additional 10-15 minutes, or until the cheese is bubbly and golden.
Once baked, remove the casserole from the oven, and let it cool for a few minutes. Serve warm, garnished with freshly chopped cilantro and lime wedges.