PREPARE pasta according to package directions, reserving 1 cup cooking water. Transfer pasta back to saucepan; add 1 tablespoon oil and 1 tablespoon butter. Season with salt and pepper. Cover and keep warm.
HEAT remaining 2 tablespoons oil with remaining 1 tablespoon butter in large skillet over medium heat. Add corn; cook without stirring for 10 to 15 minutes or until brown around edges. Add garlic; cook, stirring occasionally, for 1 minute or until corn is uniformly browned. Stir in ½ cup reserved cooking water. Cook for 2 minutes, stirring to loosen brown bits.
POUR corn mixture over pasta; toss gently to coat. Add remaining pasta water if needed. Season with salt and pepper. Sprinkle with basil. Serve with cheese.