Preheat oven to 350 degrees
In a large oven-safe pot or skillet, over med-hi heat, add olive oil, and saute chicken until browned and cooked through, remove from pan, set aside.
In same pan, over med-hi heat, melt 4 Tbsp. of butter, add angel hair pieces. Stir frequently, cook for about 3 minutes, or until all the pasta is golden brown. Add rice and seasonings, mix well.
Add water and stock, bring to a boil over high heat, reduce heat to low, cover, and simmer for 15-20 minutes. (if after twenty minutes there is still some unabsorbed water, that is okay, it will absorb during baking.)
Remove lid and quickly stir in cooked chicken pieces, and both cheeses and broccoli, reserving 2 Tbsp of the cheese for a topping after baking, if desired.
Cover with lid, and bake at 350 degrees for 20 more minutes.
Remove from oven, remove lid, sprinkle with remaining cheese, and serve.