Heat a large Dutch oven over medium-high heat. Add 2 tsp. oil; swirl. Add onion, poblano pepper, and garlic; sauté 5 minutes. Stir in flour, cumin and chili powder; cook 1 minute. Add stock, salt, tomatoes, and chopped green chilies to pan; bring to a boil. Reduce heat and simmer 7 minutes. Remove pan from heat; stir in chicken. Pour half of chicken mixture into the bottom of an 8" square baking dish; top with half of quinoa mixture and 2 oz. cheese. Repeat layers once with remaining chicken mixture, remaining quinoa, and remaining 1.5 oz. cheese. Bake at 400ºF for 25 minutes.