Heat grill. Cut tomatoes in half crosswise. With small spoon, scoop out seeds from seed cavities. Fill cavities with blue cheese. Drizzle tomatoes with oil; sprinkle with basil and Parmesan cheese. Place tomatoes, cut sides up, in disposable foil pie pan or on piece of heavy-duty foil.
When ready to grill, place pie pan on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 15 minutes or until tomatoes are thoroughly heated and begin to soften.