Cook the noodles in well-salted water according to the instructions on the packet until they are al dente.
In the meantime, cut the tomatoes into cubes and mix with the olive oil and balsamic vinegar. Chop the basil and fold into the tomato mixture. Mix the whole thing with a little salt and a lot of freshly ground pepper.
When the pasta is ready, fold the tomato mixture into the pasta and let it steep for about 1 hour.
Just before serving, dice the mozzarella and fold in, season again with pepper if necessary.