Mix the mince with some seasoning and leave to come to room temperature while you make the slaw. Slice both cabbages finely and put in a bowl. Grate the carrot coarsely and add to the cabbage. In a separate bowl, mix the mayonnaise, yogurt and mustard, season to taste, then stir into the cabbage mixture. Divide the mince into four, roll into balls and then squash into patties. Heat a heavy-based frying pan, and dry-fry the burgers for about 4 minutes on one side, flip, then cook for another 3 minutes, or longer if you prefer. Top with the sliced cheddar, grill until the cheese melts, then assemble the burgers in buns with tomato ketchup or mayonnaise if you like, and a dish of coleslaw.