Cook rice according to package instructions; set aside.
Melt butter in a large oven-proof skillet over medium high heat. Add garlic, onion, mushrooms and celery. Cook, stirring occasionally, until tender, about 3-4 minutes. Stir in thyme until fragrant, about 1 minute.
Whisk in flour until lightly browned, about 1 minute. Gradually whisk in wine and chicken stock. Cook, whisking constantly, until slightly thickened, about 2-3 minutes; season with salt and pepper, to taste.
Stir in broccoli, sour cream, chicken, 3/4 cup cheese and rice. Sprinkle with remaining 3/4 cup cheese.
Place into oven and bake until bubbly and heated through, about 20-22 minutes.
Serve immediately, garnished with parsley, if desired.