In a large heavy pot, heat corn oil and olive oil over high heat until the oil smokes. Add 1 kernel popping corn and heat until kernel pops. Add split garlic cloves and rest of popping corn, cover pot, and shake gently until corn starts to pop. Shake vigorously until popping subsides. Remove from heat. Remove garlic. Toss popcorn with provolone, tomatoes, oil, salt and chopped basil.