Cook your chicken breast. I cooked mine in my Ninja foodi on the pressure cooker setting (you could do the same using an instant pot, bake the chicken, or even just purchase a rotisserie chicken). If using pressure cooker: place the chicken breast in the pressure cooker and add in one cup of water. Set to HIGH pressure for 15 minutes and then natural release of pressure for 5 minutes before quick releasing any remaining pressure. Take the chicken out and shred with a fork. 

While the chicken is cooking, cook your long grain and brown rice according to the instructions on the package and set aside. 

Preheat the oven to 375 degrees. 

In a large cast iron skillet, heat olive oil over medium heat. 

Add in the garlic and onion and stir, cooking for about 3 minutes. 

Add in the thyme and cook for 1 minute. 

Add in the flour and stir continuously for 1 minute. 

Add in the chicken broth and continue stirring for about 3 minutes, until slightly thickened. Sprinkle on salt and pepper to taste. 

Add in the broccoli, Greek yogurt, chicken, rice, and 1/2 of the cheese - mixing well between each addition. 

Stir until well mixed and then add the remaining 1/2 of the cheese on top. 

Place the skillet in the oven and bake for 24 minutes.