1. Cut the tomatoes into halves. Peel and slice the garlic. Pick the basil leaves off the stalks and put them to one side. Finely chop the stalks. Grate the Parmesan.
2. Bring a large pan of salted water to a boil. Cook pasta according to package directions. Drain in a colander and reserve some of the cooking water.
3. When pasta is about five minutes from being done, put a large frying pan over medium heat. Add a couple of teaspoons of olive oil and the garlic. Add the butter and let it melt. When the garlic starts to brown, add the tomatoes. Stir, then add the basil stalks and half the leaves. Add the vinegar and season with salt and pepper. Add the pasta to the frying pan with a splash of the cooking water. Stir well. Taste and add a little more salt and pepper to taste.
4. Divide the pasta between your plates or bowls. Sprinkle over the rest of the Parmesan and the basil leaves, tearing any larger ones up.