Ingredients
Flour, for dusting
1 recipe Egg Pasta Dough
3 tablespoons extra-virgin olive oil, plus more for serving
1 fennel bulb, trimmed, halved lengthwise, cored, and thinly sliced crosswise (1 1/2 cups)
Kosher salt
3 cloves garlic, thinly sliced (4 teaspoons)
3/4 cup pitted mixed olives, such as Castelvetrano and Kalamata, halved
3 anchovy fillets, rinsed and patted dry
2 tablespoons capers, drained and rinsed
1/4 teaspoon red-pepper flakes, plus more for serving
1 can (28 ounces) whole peeled tomatoes in juice, drained and crushed, plus 1/3 cup reserved juices
1 1/2 ounces Parmigiano-Reggiano, grated (1/3 cup), plus more for serving
Chopped fresh oregano, for serving
Preparation
On a floured work surface, roll out one square of the rested pasta dough to an approximately 14-by-16-inch rectangle. Cut sheet into 2-inch squares. Keep squares covered with plastic wrap to keep from drying out.
Starting at one corner of each square, roll dough around a wooden dowel, chopstick, clean pencil, or other small rod that averages about 3/8-inches in diameter. Slide pasta tube off dowel and transfer to a rimmed baking sheet dusted with semolina. Repeat with remaining dough.
Heat 3 tablespoons oil in a large straight-sided skillet over medium-high. Add fennel, season with salt, and cook, stirring occasionally, until tender and golden brown in places, 8 to 10 minutes. Add garlic, olives, anchovies, capers, and red pepper flakes; cook until fragrant, 2 to 3 minutes. Add tomatoes and reserved juices; simmer until thickened slightly, 4 to 5 minutes.
Meanwhile, cook pasta in a large pot of generously salted boiling water until al dente, 4 to 5 minutes. Reserve 1 cup pasta water; drain. Add pasta and 1/2 cup pasta water to puttanesca, tossing to combine.
Cook over medium-high heat, gently tossing a few more times, until sauce clings evenly to pasta, 2 to 3 minutes. Remove from heat and stir in cheese. (If sauce is too thick, add more pasta water, a little at a time.) Transfer to bowls and garnish with oregano and a drizzle of oil. Serve with more cheese and red pepper flakes on the side.