In the bowl of your slow cooker, combine the rice, onion, carrots, broth, wine, thyme, bay leaves, paprika, crushed red pepper, parmesan rind, and a pinch each of salt and pepper. Cover and cook on low for 6-8 hours. During the last 30 minutes of cooking, stir in the 1/2 cup grated parmesan and the milk. Cook until warmed through. Remove the bay leaves and discard.About an hour before serving, preheat the oven to 425 degrees F. In a 9x13 inch baking dish, combine the mushrooms, garlic, butter, thyme sprigs, lemon zest, and a pinch each of salt and pepper. Transfer to the oven and roast for 40-45 minutes, stirring halfway through cooking, until the mushrooms are golden and caramelized. Mash the garlic with a fork, and then stir the mushrooms, mashed garlic, and any butter left into the soup. Divide the soup among bowls and top with fresh thyme and parmesan. Eat!