To make the coleslaw: In a large bowl, whisk the mayonnaise with the onion, vinegar, sugar, celery seed, cabbage, and carrot. Season with salt and pepper, and toss well. Let stand about 25 minutes.
To make the burgers: Preheat grill or skillet. Form the beef into 4 patties; rub with oil, and season with salt and pepper. Grill on high heat, turning once, for 5 minutes for medium-rare. Brush with ½ cup of the barbecue sauce. Grill the buns, and brush with the remaining barbecue sauce. Top the burgers with pickles.