Preheat oven to 350°F.
In a soup pot or Dutch oven, melt butter over medium heat. Add diced onion and cook for about 4 minutes until softened. Add garlic and cook 90 seconds more.
Stir in uncooked rice and chicken broth. Bring to a boil, then cover and reduce heat to simmer. Cook for 6–8 minutes until about half the liquid is absorbed.
Add broccoli florets to the pot, cover again, and cook for another 6–8 minutes until the rice is tender and no liquid remains. Remove from heat and let stand, covered, for 6–8 minutes.
Stir in diced chicken, cream of chicken soup, cream, sour cream, Dijon mustard, nutmeg, salt, pepper, and half the shredded cheddar cheese until well combined.
Transfer the mixture to a lightly greased 9x13 casserole dish. Sprinkle the remaining cheddar cheese evenly on top and cover with foil.
Bake covered for 15 minutes.
While baking, melt the butter for the topping and mix with crushed Ritz crackers and thyme.
Remove the casserole from the oven, uncover, and sprinkle the cracker topping evenly over the cheese layer. Bake uncovered for an additional 15 minutes until topping is golden and casserole is bubbly.
Let the casserole rest for 5–10 minutes before serving.