1. Divide and press into 8 disks. Place pork in a medium bowl; season with salt and pepper. Using hands, mix in Worcestershire until just combined; do not overmix. Divide pork into 8 patties. Press a cheese disk into center of each. Shape pork up and around cheese; carefully flatten into 1/2-inch-thick burgers, keeping cheese completely enclosed. Chill, loosely covered, until firm, about 1 hour.Make BBQ Onions::
2. Meanwhile, heat oil in a large saucepan over moderately high heat. Add onions and garlic; sauce, stirring occasionally, until onions are golden brown, about 10 minutes. Add chili powder and cook, stirring, 1 minute. Add remaining ingredients and simmer, stirring, until thickened and glazed, about 2 minutes. Remove pan from heat and cool. (Can be stored in an airtight container, chilled, up to 2 weeks. Serve at room temperature.)
3. Preheat grill and lightly oil rack. Grill burgers on rack over moderate heat, turning once, until cooked through, about 10 minutes. Meanwhile, grill buns, cut side down, until golden brown, about 1 minute. Arrange burgers in buns with BBQ Onions and serve slaw on the side, if desired. Makes 8 servings.