Place the sugar, salt, bay leaves, vinegar, allspice, and pepper in a small pot and bring to a boil. Let cook for five minutes.

Add the cabbage and onions (adding more water, if necessary) and let cook for three to four minutes. Turn off the heat and cool completely.

Store with the juice in a nonreactive container.

Mix the ground meat with the salt, pepper, and ketchup. Form into small patties. Preheat a grill pan and grill on each side until cooked through, about five minutes on each side.

Prepare large leaves of romaine lettuce. Place a burger in the center, along with the pickled vegetable mixture and any other desired condiments, such as ketchup, duck sauce, or pickles. Wrap the leaves around the burger and enjoy.