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1
Make the barbecue sauce: Heat the butter in a heavy saucepan over medium heat.
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2
Add the onion and garlic and cook, stirring, until softened, about 10 minutes.
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3
Add the ketchup, Worcestershire sauce, mustard, vinegar, brown sugar, chili powder, and hot pepper sauce, and simmer the mixture, stirring occasionally, for 15 minutes.
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4
Transfer the sauce to a bowl and let it cool.
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5
The barbecue sauce may be made 4 days in advance and kept covered and chilled.
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6
Make the burgers: In a bowl combine well the pork, the bread crumbs, and 1/3 cup of the barbecue sauce and form the mixture into 4 (1-inch-thick) patties.
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7
Lightly brush the burgers with oil and season with salt and pepper.
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8
Heat a well-seasoned grill pan over medium-high heat.
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9
Grill the burgers, turning once, until just cooked through, about 6 minutes per side.
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10
Baste the burgers with some of the barbecue sauce and continue to grill, turning and basting occasionally, for 2 minutes more
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11
While the burgers are grilling, make the coleslaw: In a bowl combine the cabbage, carrot, onion, lemon juice, mayonnaise, and salt and pepper, to taste.
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12
Transfer the burgers to the buns and top them with the coleslaw.
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13
Serve the remaining barbecue sauce separately.
