Pour one cup of rice into baking dish, evenly distributing the rice.
In large skillet, heat 2 tbsp of olive oil over medium to medium-high heat. Add onion. Stir and continue cooking until onions are darkened and caramelized, about 5 minutes. Add garlic. Remove pan from heat momentarily and slowly and carefully stir in beef broth to prevent splattering (and injury). Return to heat and continue cooking, stirring occasionally until mixture is thickened and dark—this will take another 5 minutes or so. Once the mixture looks like that rich, delightful concoction that is French onion soup, pour it over the rice in the baking dish. Slowly add water to the rice mixture. (You can do this in one corner of the dish so as not to disturb the onion mixture you’ve already evenly distributed over the rice.)
At this point, preheat your oven to 350 degree Fahrenheit.
Using the same skillet (you don’t need to clean or wipe it), add another tablespoon of oil (or butter) and heat up a bit. Slowly stir in flour until smooth. Remove from heat momentarily and slowly and carefully stir in beef broth to prevent splattering (and injury). Return to heat and gradually add milk. Stir in mushrooms. Bring to a gentle boil. Stir until thickened.
Place chicken pieces over rice mixture. Sprinkle pepper over chicken breasts to taste. (I used a peppercorn medley that I've been enjoying. It included several varieties of peppercorns as well as coriander. I added maybe ½ teaspoon. No salt was needed because of sodium in beef broth.)
Spoon mushroom mixture over chicken pieces.
Bake at 350 degrees Fahrenheit for an hour and a half if using large chicken breasts, or less if using smaller pieces of chicken. I checked every half hour to see if additional water was needed and did add some. I also covered the dish with aluminum foil for the last hour of cooking.
Recipe by gfe--gluten free easily at http://glutenfreeeasily.com/chicken-and-rice-casserole%e2%80%94uncondensed/