Barbecued Pork Burgers with Slaw

INGREDIENTS

• 1 1/2 pounds ground pork
• 1/4 cup mayonnaise
• 1 tablespoon thinly sliced fresh chives
• 1/2 cup very finely shredded carrot (1 medium)
• 1 tablespoon milk
• 1/2 cup bottled tomato-based barbecue sauce
• 1 (1/2-pound) piece green cabbage, cored
• 1 tablespoon plus 1 1/2 teaspoons white-wine vinegar, divided
• 1/4 teaspoon cayenne
• 4 kaiser or soft rolls, split and grilled