1. In a wide, shallow bowl, combine the olive oil and next 5 ingredients (through pepper).
2. Add tomatoes, and turn to coat them on all sides.
3. Prepare grill.
4. Place tomatoes, cut sides down, on the grill rack. Brush once with remaining marinade, and then discard marinade. Grill about 5-7 minutes on each side over medium-high heat or until tomatoes begin to blister, soften, and brown. (They can burn easily, so keep an eye on them.)
5. Remove the tomatoes from grill, and top with Parmesan cheese, if desired, and parsley. Serve immediately.