Place the butter in a saucepan and melt slowly. Add the onion, garlic and mushrooms and sauté for 3 minutes (do not allow to burn). De-glaze the pan with the rum or wine and allow to cook for 2 minutes more.
Transfer the mushroom mixture to a large mixing bowl and mix in the beef, jerk seasoning and parsley. Season with salt and pepper. Form into 6 fat patties