Light a grill. In a bowl, combine the ground chuck and sirloin. Form the meat into eight 3-ounce patties and season both sides with salt and black pepper. In a mini food processor, blend the cheese with the mayonnaise, mustard and cayenne pepper until smooth. Add the pimentos and pulse to combine. Spoon the pimento cheese in the centers of 4 of the patties and cover each with the remaining patties, pinching the edges to seal completely. Flatten the stuffed burgers into 4-inch rounds.
Brush the burgers very lightly with oil and grill over high heat, turning once, until medium rare, about 6 minutes. Just before the burgers are done, toast the buns. Set the pickle chips on the bottom halves of the buns, top with the burgers and coleslaw and serve.