In a 1- to 2-quart pan over high heat, bring wine and pickling spice to a boil. Remove from heat and let cool to room temperature, about 45 minutes. Pour through a strainer into a large bowl; discard solids.
Add ground pork, salt, pepper, cinnamon, and nutmeg to bowl. Mix very thoroughly with your hands to distribute spices evenly.
Shape about 1/3 cup (about 3 oz.) pork mixture into an oval-shaped patty about 1/2 inch thick. Place on a waxed paper-lined baking sheet. Repeat to shape remaining mixture into patties, stacking them in layers separated by sheets of waxed paper.
Lay patties on a grill over medium-hot coals or medium-high heat on a gas grill (you can hold your hand at grill level only 4 to 5 seconds); close lid on gas grill. Cook patties, turning once, until browned on both sides and no longer pink in the center (cut to test), about 8 minutes total. (Alternatively, fry patties in a 10- to 12-inch frying pan over medium heat, turning as needed, until browned on both sides and no longer pink in the center, 10 to 15 minutes total.) Pile on a platter and serve.