Combine rice, chicken broth, broccoli, onion, cream cheese and shredded cheese in a 13 x 9 baking dish. Place in oven and bake for 15 minutes.
Combine seasonings for chickens and sprinkle evenly over both sides of chicken. Add oil to large saute pan over medium-high heat. Once hot, cook each piece of chicken on each side for 4 minutes. Cook in batches if you need to. Do not clean out pan when done but remove from heat.
Remove baking dish from oven and stir to combine. Place chicken in a single layer over and return to oven. Bake for 30 minutes.
In the last 15 minutes of bake time, return saute pan to medium heat. Add butter, garlic powder and thyme. Once melted, whisk in flour and let cook for 3 minutes. Whisk in chicken broth and salt. Cook for another 4 minutes then reduce heat to simmer until chicken and rice is taken out of oven.
Serve a portion of rice and broccoli with a piece of chicken. Ladle pan gravy over top of chicken.