Preheat oven to 375°.
Add rice to a saucepan with 3 cups of chicken broth. Bring to a boil. Cover and lower to simmer for 10 minutes.
Add broccoli over rice but do not stir. Cover and continue to cook 5 minutes.
Meanwhile, in a casserole dish, whisk together sour cream, heavy cream, remaining 1/2 cup of chicken broth, mustard, rosemary, salt and pepper.
Mix in diced chicken, water chestnuts, green onions and half of cheese.
Stir in cooked rice and broccoli and mix until well combined.
Top with remaining cheese.
Bake 15 minutes.
Meanwhile, combined crushed Ritz crackers with crumbled bacon and butter.
Remove from oven and sprinkle cracker and bacon mixture evenly over casserole.
Return to oven for 10 -15 minutes until cracker crumbs are toasted and edges of casserole are bubbly.