Add prosciutto to the pan and cook, scraping up any browned bits, for 30 seconds. Add the remaining 1 tablespoon oil and mushrooms; cook, stirring occasionally, until tender, about 4 minutes. Stir in shallots, garlic, thyme and the remaining 1/4 teaspoon pepper and 1/8 teaspoon salt; cook, stirring often, until the shallot is translucent, about 1 minute. Stir in broth, cream and Marsala, scraping up any browned bits. Cook until slightly reduced, about 2 minutes.