Place porcini mushrooms in small bowl. Pour 2 cups hot water over. Let stand until mushrooms soften, about 25 minutes. Using slotted spoon, transfer mushrooms to work surface and coarsely chop. Reserve soaking liquid.
Heat olive oil in heavy large pot over medium-high heat. Add porcini, crimini and portobello mushrooms, minced garlic and bay leaf. Sauté until mushrooms are brown and tender, stirring often, about 10 minutes.
Add Marsala and simmer until almost all liquid evaporates, scraping up browned bits, about 1 minute. Season mushroom mixture to taste with salt and pepper.
Mix 1 cup reserved mushroom liquid and whipping cream into mushroom mixture and simmer 3 minutes. Add 1 cup Parmesan cheese and butter. Cook, stirring frequently, about 2 minutes. Season to taste with salt and pepper.
Serve over polenta, pasta or rice passing additional grated Parmesan separately.