Cook the rice mix according to package instructions; set aside.
Melt the butter in a large ovenproof skillet over medium-high heat. Add the garlic, onion, mushrooms, and celery and cook, stirring occasionally, until tender, 3 to 4 minutes. Stir in the thyme and cook until fragrant, about 1 minute.
Whisk in the flour until lightly browned, about 1 minute. Gradually whisk in the wine and chicken broth. Cook, whisking constantly, until slightly thickened, 2 to 3 minutes; season with salt and pepper to taste.
Stir in the broccoli, sour cream, chicken, 1/2 cup of the cheese, and the rice. If you want to freeze the casserole, you can stop here and skip to step 7. Otherwise, sprinkle with the remaining 1/2 cup cheese.
Transfer the skillet to the oven and bake until the casserole is bubbly and heated through, 20 to 22 minutes. Serve immediately, garnish with parsley, if desired.
To freeze, transfer the unbaked casserole mixture to a ziplock freezer bag and lay the bag flat in the freezer. Freeze for up to 3 months. When ready to serve, thaw overnight in the refrigerator. To cook, transfer to an ovenproof skillet or baking pan, sprinkle with 1/2 cup cheddar cheese, and bake at 375 degrees F for 20 to 30 minutes, or until heated through.
*If you don't have white wine, you can use all chicken broth.* Recipe from Damn Delicious Meal Prep by Chungah Rhee.