In a large skillet, heat the 2 tablespoons of olive oil over medium heat. Add the finely chopped onion and sauté until translucent, about 3-5 minutes.
In the skillet, add the cooked quinoa, shredded chicken, black beans, and green chiles. Pour in the enchilada sauce and mix everything together. Allow the mixture to heat through for about 5 minutes, stirring occasionally.
Preheat your oven to 375°F (190°C). In your 9x13 inch baking dish, layer half of the quinoa mixture, then sprinkle with half of the cheddar cheese and mozzarella cheese. Repeat the layers with the remaining quinoa mixture and top with the rest of the cheeses.
Cover the baking dish with aluminum foil and bake in the preheated oven for 20 minutes. Then, uncover and bake for an additional 10-15 minutes, or until the cheese is bubbly and golden brown.
Once baked, remove the casserole from the oven and let it cool for a few minutes. Serve with a dollop of sour cream, a sprinkle of fresh cilantro, and a squeeze of lime juice for bright flavor.