Bring 6 quarts of water to a rolling boil and add 2 teaspoons salt.
In a bowl, combine the garlic, anchovies, tomatoes, parsley, chili flakes, and the extra-virgin olive oil. Mix well.
Cook the pasta according to the package directions until just al dente and drain. Refresh in an ice bath until cool and drain well. Toss with 2 tablespoons extra-virgin olive oil to prevent sticking. Mix the cool pasta with the room temperature tomato sauce, pour the pasta into a serving dish, sprinkle with the remaining parsley and add Parmigiano-Reggiano, to taste. Serve immediately.