In a saucepan, bring the water to a boil with half of the salt, reduce the heat, cover, and simmer for about 45 minutes, until the rice is tender and has absorbed the water.
When rice cooks and is about halfway done, butter casserole dish. In a large pot, melt 3 tablespoons butter and flour over medium heat until golden in color to make a quick roux.
Add mushrooms, onion, garlic, garlic powder, cayenne pepper, heavy cream, and vegetable broth. Add broccoli, half of the cheese, and rice. Season with salt and pepper, to taste.
Pour into buttered dish and top with remaining shredded cheese. Bake until cheese is melted and golden, about 20 minutes.