Cook the pasta al dente. Drain, reserving about half ½ cup of the pasta cooking water (!).
Using a sharp knife, slice a shallow X into the bottom of the tomato. Pour boiling water over the tomatoes, peel them and cut into ½ inch / 1.5 cm cubes.
Peel and cut the garlic into thin slices.
Heat the olive oil and butter in a large frying pan, add the garlic, cook over medium heat for about a minute.
Add the tomatoes and lemon zest, cook for a few minutes, the tomatoes should stay mostly chunky, but will release their juices a bit and they will, together will the olive oil and butter, form a sauce.
Add the lemon juice and a few tablespoons of pasta cooking water, just enough to thin the sauce a bit.
Remove the pan from the heat, add the cooked pasta, torn into smaller pieces mozzarella. Toss everything together, season with salt and pepper to taste.
Sprinkle with basil leaves, transfer to plates, serve warm.