Place onion, brown rice, Dijon mustard, garlic powder, dried thyme, salt and pepper in bottom of slow cooker.
Pour in broth and stir until well combined.
Add chicken to the slow cooker. Sprinkle chicken with additional black pepper.
Cover and cook on high for 2 1/2 to 3 1/2 hours, until chicken is cooked through and rice has absorbed almost all of the broth. In my slow cooker this took 3 hours on high.
When the slow cooking time is almost finished, cook the broccoli. You can steam it on the stove or in the microwave, or roast it in your oven. (It is also possible to cook the broccoli in the slow cooker by adding it on top of the rice and chicken during the last hour of cook time. If you slow cook the broccoli it will lose its vibrant green color. I get best results when I steam the broccoli on the stove.)
When chicken and rice are done, remove chicken to a cutting board.
Add the plain Greek yogurt (if using), Parmesan cheese and cheddar cheese to the rice in the slow cooker. Stir to combine.
Cut the chicken into bite-size pieces and add to the slow cooker along with the cooked broccoli. Stir and serve.