Peel, halve, and pit the peaches and cut into 1/8-inch-thick slices. Heat the oil and butter in a sauté pan over high heat. When the butter foams, add the peaches, mushrooms, and onion and cook, stirring occasionally, for 3 to 4 minutes, or until glossy. Add the stock, vinegar, and cream and boil for 1 to 2 minutes, or until reduced by about half. Stir in the parsley and season with salt and pepper. Serve in small bowls or plates.