Combine the mozzarella, tomatoes, basil and 3 tablespoons olive oil in a large mixing bowl; season generously with salt and pepper. Set aside to allow the flavors to marry.
Using an 8-quart stock pot with a pasta insert, bring 4 to 6 quarts of water to the rolling boil.
Add the kosher salt and bring back to the boil. Add the farfalle and immediately stir to separate the individual pieces. The water should return to the boil very quickly. If necessary, cover the pot until the water returns to the boil. Cook just until al dente, stirring the pasta once or twice during cooking. Drain thoroughly and immediately toss with the mozzarella tomato mixture; drizzle with the basil oil. Taste and adjust the seasoning as needed, then sprinkle with grated Parmesan and serve immediately
* To cut the pasta into farfalle: Roll the pasta dough through the pasta machine starting at the #1 setting and graduating to the #6 setting. Cut the pasta sheets into 1-inch wide strips using a pastry wheel or a chef's knife. Cut the 1-inch wide strips into 2-inch lengths using a fluted pastry cutter.
Pinch each rectangle in the center to form the farfalle. Allow the farfalle to dry for 5 to 10 minutes before cooking.