With machine running, drop garlic through feed tube of food processor to mince. Stop, add fresh basil, and process until chopped. Add lemon juice, oil, salt, and pepper and process to make thin wet rub. Spread both sides of pork chops with basil mixture. Let stand 15 to 30 minutes.
Prepare a medium-hot fire in grill. Brush the grate clean and oil the grate. Grill chops, over direct heat, turning once, to medium rare doneness, 5 to 6 minutes per side, or until the internal temperature reaches 145 degrees Fahrenheit, followed by a 3-minute rest time.
Top the chop with shavings of Parmesan cheese (shave from a wedge of cheese with a vegetable peeler) and toasted pine nuts, if desired. Serve with slices of ripe tomatoes and mozzarella on a bed of arugula drizzled with balsamic vinegar and olive oil.