How to Make It
Heat oil in a large, high-sided skillet over medium. Add onion, and cook, stirring occasionally, until slightly softened, about 4 minutes. Stir in squash and salt. Cook, stirring occasionally, until squash begins to soften, about 10 minutes. Stir in crushed tomatoes. Cover and reduce heat to medium-low. Cook, stirring occasionally, until squash is tender, 8 to 12 minutes.
Meanwhile, bring 4 quarts water to a boil in a large saucepan over high. Stir in 1/4 cup salt. Add pasta, and cook, stirring occasionally, until tender, 2 to 3 minutes. Using tongs or a spider, transfer cooked pasta to tomato mixture in skillet, reserving 1 cup pasta cooking liquid.
Increase heat to medium, and cook pasta mixture, stirring constantly and adding reserved cooking liquid, 1/4 cup at a time, until sauce clings to pasta, 2 to 3 minutes. Stir in provola affumicata. Season with salt to taste. Divide mixture among serving bowls. Top evenly with Parmigiano-Reggiano, and garnish with parsley.
Find the Italian cheeses called for in this recipe at specialty cheese shops.