How to Make It
In a food processor, pulse the flour with the salt a few times. In a medium bowl, beat the eggs with the olive oil. With the machine on, pour in the eggs and process until a smooth, sticky dough forms. Scrape the dough out onto a lightly floured work surface and knead until smooth. The dough will be soft and still slightly tacky. Transfer the dough to a medium bowl and rub the surface with olive oil. Cover with plastic wrap and let stand at room temperature for at least 30 minutes.
Divide the dough in half. On a lightly floured surface, roll out 1 piece to a rectangle about 1/8 inch thick. Cut the dough in half. Using a pizza cutter, cut the dough into 6- to 8-inch-long strands 1/3 inch wide. Dust 2 large baking sheets with cornmeal and carefully lay the strands on the sheets; sprinkle the strands with cornmeal to prevent sticking. Repeat with the remaining dough. Cover and set aside at room temperature.
Fill a large bowl with water and squeeze a lemon half into it. Working with 1 artichoke at a time, snap off the outer leaves. Using a sharp knife, cut off the top two-thirds of the leaves and trim the base and stem. Using a melon baller or teaspoon, scoop out the furry choke. Rub the artichoke heart all over with the remaining lemon half. Slice the heart 1/4 inch thick and put in the bowl of lemon water. Repeat with the remaining 3 artichokes.
Drain the artichokes. In a medium saucepan, combine the artichokes with the stock, wine, garlic, tomato paste, olive oil and crushed pepper; season with salt and pepper and bring to a boil. Simmer over low heat, stirring a few times, until the artichokes are just tender and the sauce has thickened slightly, about 30 minutes. Season the sauce with salt and pepper and keep warm.
Bring a large pot of salted water to a boil. Add the pasta and cook, stirring, until al dente, about 5 minutes. Drain and transfer to a large, wide pasta bowl. Spoon the sauce over the pasta and toss well. Sprinkle with the Pecorino, basil and parsley and serve at once.