Variations: Cook’s Country offers a simple puttanesca variation: Add 2 minced anchovies to skillet with garlic and increase pepper flakes to ½ teaspoon. Substitute ½ cup red wine for ½ cup of water. Substitute fresh parsley for the basil and stir ½ cup chopped pitted olives and 2 tablespoons minced capers into the cooked pasta along with the Parmesan.
Other ideas include: adding finely chopped kale, Swiss chard or spinach to the cooked pasta, which will incorporate easily and up the veggie quotient. Another idea is to add roasted eggplant or sautéed zucchini or other vegetables to the cooked pasta. For a richer variation, replace some of the water with heavy cream.
Adjust oven rack 6 inches from broiler element and heat broiler. Heat 12-inch cast-iron skillet (or other large oven-safe skillet) over medium heat for 5 minutes. Toss tomatoes with oil and 1 teaspoon salt. Add tomatoes to skillet and cook, stirring occasionally, until lightly charred and blistered, about 10 minutes. Stir in garlic, tomato paste, and pepper flakes and cook until fragrant, about 30 seconds. Off heat, coarsely mash tomatoes using potato masher.
Stir in pasta and water and bring to boil over medium-high heat. (I add another teaspoon of kosher salt at this point, and more later, but if you are sensitive to salt, maybe start with 1/2 teaspoon.) Reduce heat to a vigorous simmer (low heat), stir well, cover, and cook, stirring every few minutes, until pasta is tender, 15 to 18 minutes.
Stir in Parmesan and adjust sauce consistency with extra hot water as needed. Stir in basil. Taste—this is your chance to get the seasoning right. Add salt and pepper to taste (I add another 1/2 teaspoon kosher salt and lots of fresh pepper). Sprinkle with mozzarella. Transfer skillet to oven and broil until cheese is melted and spotty brown, about 5 minutes. Serve.