Preheat oven to 325. Grease 3 quart casserole dish.
Heat 1 tablespoon oil in a large skillet over medium heat. Add broccoli, onion, and pepper. Cook 3 minutes and remove from skillet. Set aside.
In the same skillet, add remaining 2 tablespoons oil. Add flour and stir constantly. Slowly stir in milk, broth, and cumin. Bring to a simmer, stirring constantly. Remove from heat.
Add green chiles, broccoli mixture, chicken, 1 cup cheese, and pasta to sauce in pan. Stir well.
Add chicken mixture to prepared casserole dish. Cover, and bake at 325 for 25 minutes. Top with remaining cheese and bake an additional 10 minutes.