Split the rolls and spread the cut sides with the butter. Grill until toasted and golden, about 2 minutes.
Mix the ground pork with the rub in a bowl until just combined. Form into 4 rectangular patties, slightly larger than your rolls.
Lightly oil the grill grates. Place the patties on the grill and cook for 3 minutes. Flip the patties and baste with barbecue sauce. Cook until charred on the other side, another 3 minutes. Continue this process multiple times, flipping and basting about every 3 minutes, until both sides are glossy and charred and the internal temperature hits 165 degrees F, 5 to 8 minutes.
Place the patties on the rolls and top with the dill pickles, red onions and additional barbecue sauce, if desired.