Heat a large 12 inch ovenproof skillet or 8 quart dutch oven over high heat. Add oil and butter and once heated, add chicken. Allow to cook for a few minutes until it turns golden brown. Add onion and mushrooms, stir, and cook until most of the liquid has cooked out, 5-10 minutes.

Cook rice according to package directions; drain.

Cook broccoli in microwave by added a tablespoon of water, covering bowl with a plate, and heating on high for 2 minutes. Drain off any excess water.

Combine milk and flour, stirring with a whisk or fork until smooth.

Stir milk mixture into chicken mixture in skillet.

Cook 2 minutes or until bubbly and thick, stirring frequently.

Stir in rice, broccoli, and half of the shredded cheese, along with the salt and pepper.

Top with remaining cheese.

Preheat broiler to high and broil 1 minute or until cheese melts and just begins to brown.