If you are not freezing this meal, preheat your oven to 350.
In a saucepan, add the butter over medium heat.
Once the butter is melted, add the flour and stir and cook until it just starts to brown.
Add the stock and milk all at once.
Cook and stir continuously until mixture thickens. If it's too thick, add more stock or milk. If it's too thin, keep cooking until it's the desired thickness like soup.
Season with salt and pepper and set to the side.
Place 4 cups of water in a large pot and heat over medium high heat.
Once the water boils, add in your rice and a pinch of salt and reduce to simmer.
Cover the rice.
Check rice for doneness at 18 minutes.
Remove from heat and leave lid on for another 5-10 minutes.
Fluff up rice.
While the rice is cooking, place a skillet over medium heat.
Add olive oil and your diced chicken.
Sprinkle on a pinch of salt and pepper.
Saute until browned.
In a large bowl or a 9 x 13 casserole dish, add rice, cooked chicken, broccoli, thyme, and sauce.
Mix everything until combined.
Top with shredded cheddar cheese.
Cover your casserole dish.
Cook for 20-30 minutes.