Fill a large stock pot with water and place it over medium-high heat. Bring the water to a boil. While you are waiting for the water to boil, start your sauce.
Place the tomatoes and olive oil in a saucepan over low heat. Add the onion cut sides face down. Simmer the sauce for 30-45 minutes. As the sauce cooks, gently break up the whole tomatoes with the back of a wooden spoon. When the sauce is finished cooking, about 20 minutes, remove the onion and discard. Taste and season with sea salt as necessary. Set the sauce aside.
Once the pasta water is boiling, season it with sea salt. Pour in the pasta and cook until al dente. Toss drained pasta with the tomato sauce. Scoop pasta into individual bowls and top with the fresh mozzarella torn into small pieces and the basil leaves. Eat immediately!