Heat oil over medium heat in large saucepan. Add onion, garlic, celery, and carrots. Saute until soft, about 6-8 minutes. Add basil, tomatoes, and bay leaves. Season with salt and pepper. Reduce to low heat, cover, and simmer for 1 hour. Add butter, and remove bay leaves.
Process sauce in blender or food processor, in batches, until smooth.
Add vodka to tomato sauce and simmer or low for an additional 30 minutes. Sauce will reduce and thicken. Stir in cream and Parmesan and simmer until cheese is melted and sauce blended.
Cook pasta to al dente in boiling, salted water. Drain and transfer to large bowl. Pour sauce over cooked pasta and toss. Serve immediately.