In a small bowl, stir together the mayonnaise, lime juice and ground cumin. Set aside.
In a medium bowl, combine the ground pork and grill seasoning. Form into 6 patties.
Preheat a stovetop grill over medium-low heat. In a large nonstick skillet set over medium heat, cook the patties for 6 minutes per side. During the final 2 minutes, top each patty with an equal amount of ham and cheese. Cover the skillet and cook until the cheese melts.
Spread the mayonnaise mixture on the cut sides of each roll. Place a patty on each roll bottom, top with 1/3 cup shredded lettuce, 3 pickles and set the roll top into place.
Arrange the burgers on the grill. Weight the burgers using a heavy pan, such as a cast-iron skillet. Cook until crispy and grill marks appear, 1 to 2 minutes. Flip the burgers and repeat.