1 (1/2-lb) piece green cabbage, cored
1/4 Cup mayonnaise
1 Tbsp milk
1 Tbsp plus 1-1/2 tsp Traditional White Balsamic Vinegar, divided
1/2 Cup very finely shredded carrot (1 med carrot)
1 Tbsp thinly sliced fresh chives
1/2 Cup of your favorite barbecue sauce (we like our Jalapeno Balsamic BBQ Sauce best!)
1/4 tsp Cayenne Pepper
1-1/2 lbs ground pork
4 kaiser or soft rolls, split and grilled
Prepare grill for direct-heat cooking over medium-hot charcoal (medium heat for gas).
Thinly slice enough cabbage with slicer to measure 2 cups. Whisk together mayonnaise, milk, and 1-1/2 tsp vinegar until smooth, then toss with cabbage, carrots, chives. Add salt and pepper to taste. Let coleslaw stand at room temperature, uncovered, while making burgers.
Stir together barbecue sauce, cayenne pepper, 1/4 tsp salt, and remaining Tbsp vinegar until combined well.
Mix together ground pork, 1/2 tsp salt, 1/4 tsp pepper, and 2 Tbsp barbecue sauce mixture until combined (do not overmix). Form mixture into 4 (3/4-inch-thick) burgers (4 inches in diameter).
Oil grill rack, then grill patties, covered only if using a gas grill, turning over occasionally, until just cooked through, about 6 min total.
Brush top of each patty with 1 Tbsp barbecue sauce mixture, then turn over and grill 30 seconds. Brush top of each patty with 1 Tbsp barbecue sauce, then turn over and grill 30 seconds more.
Brush cut sides of rolls with remaining 1/4 cup barbecue sauce, then pile sandwich patties and coleslaw between rolls.