Saute garlic, onion, and mushrooms in large pot. Once golden, add thyme, parsley, chicken stock, paprika, and nutmeg. Simmer 15 minutes; remove; puree. Return to pot; boil. Add cream, reduce for 5 minutes. Season with salt and pepper; keep warm.
Saute remaining mushrooms (caps only); season. Divide soup into four bowls; add a slice of pecorino in center of each; top with mushrooms. Serve.