Heat barbecue to medium-high heat.
Using a mortar and pestle, combine salt, caraway seeds, peppercorns and sugar; grind until fine. Add paprika, garlic and marjoram; grind again until fine. Rub all over pork chops and let marinate at room temperature for 15 minutes.
Using a sharp bread knife, make 6 deep cuts across each bread roll without cutting through to make a grid pattern. In a bowl, stir parsley, mozzarella, garlic and ¼ cup of the olive oil. Drizzle ¼ cup remaining olive oil into cuts; fill into ruts and sprinkle with salt and pepper.
Brush pork chops with sunflower oil; place on greased grill. Cook, covered flipping once, until juices run clear when pork is pierced and just a hint of pink remains inside, 5 minutes per side. Place bread rolls on grill; cook, covered, until crisp and cheese is melted, about 5 minutes.
Transfer pork chops to cutting board; cover with foil and let stand for 3 minutes before serving with bread rolls.