Preheat grill by turning it on to high and sit for 5 minutes. Scrape rack with a wire brush to remove any residue.
In a medium bowl, combine the pork, shredded cheese and seasoning. Mix with hands until completely incorporated.
Divide the meat evenly into 4 balls and flatten into round patties.
Place on a plate and baste both sides of each patty with the olive oil. Add more olive oil, if necessary.
Lower the grill heat to medium and place the patties onto the rack. Cover and cook for 7 - 10 minutes on each side, until the temperature registers 160° F. when a meat thermometer is inserted horizontally into the middle of each.
Serve on buns and top with barbecue sauce, lettuce, tomato, and red onion, if desired.