Toss the tomatoes in a large bowl with 2 tablespoons olive oil, the vinegar and a large pinch each of salt and pepper; set aside to marinate.
Meanwhile, bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1/2 cup cooking water, then drain. Add the warm pasta to the tomatoes along with the salami and 1/4 cup of the reserved cooking water; stir to combine.
Add the remaining 1 tablespoon olive oil, the mozzarella, basil and parsley to the pasta; toss until combined and slightly saucy. Add the remaining reserved cooking water as needed to loosen, 1 tablespoon at a time. Season with salt and pepper.