In a large bowl, whisk the mayonnaise with the onion, vinegar, sugar and celery seeds. Add the shredded cabbage and carrot, season with salt and pepper and toss well. Let stand until slightly softened, about 25 minutes.
Light a grill. Form the beef into 4 patties; rub with oil and season with salt and pepper. Sear over high heat, turning once, for 5 minutes for medium-rare. Brush with 1/2 cup of the barbecue sauce and grill until glazed, about 1 minute per side.
Grill the buns and brush them with the remaining barbecue sauce. Top with the burgers, pickles and coleslaw and serve.
Smoky, full-bodied Texas bock beer.
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