In a large skillet, melt the butter and cook the onion and garlic until onion is wilted. Add the pork and cook, breaking up the meat with a slotted spoon. Cook until the pork loses color. Add the mushrooms and cook, stirring, for 3 minutes more. Add the bread crumbs, salt, pepper, parsley, and rosemary. Spoon equal amounts of the mixture into the pepper cases. Sprinkle equal amounts of cheese onto the stuffing and arrange the peppers in a baking dish. Pour the water or tomato sauce around them and bake until peppers are tender, about 25 minutes.