1. Combine first 5 ingredients in a large zip-top plastic freezer bag; add tomatoes, seal, and shake gently to coat. Chill 1 hour.
2. Preheat grill to 350° to 400° (medium-high) heat. Remove tomatoes from marinade, reserving marinade. Grill tomatoes, covered with grill lid, 3 to 4 minutes on each side or until tender and grill marks appear.
3. Arrange alternating slices of warm grilled tomatoes and mozzarella cheese on a large, shallow platter. Drizzle with reserved marinade; season with salt and pepper to taste. Sprinkle with basil.