Preheat oven to 350°. Melt butter in a 2-quart stovetop-to-oven covered skillet or casserole dish on medium heat. Add onions and cook until tender; 5 minutes. Add mushrooms and garlic and cook until mushrooms are lightly browned; 5 to 8 minutes. Add rice and spices and stir until incorporated. Add broth. Bring to a boil; cover and transfer to oven. Bake in the oven until the rice is tender and the stock is absorbed, about 45 minutes to 1 hour. Let stand, covered, for 10 minutes. Serve.