How to Make It
In a food processor, pulse the flour with 1 teaspoon of salt. With the machine on, add the eggs and process until the mixture resembles wet sand. Transfer the dough to a work surface and knead until smooth. Roll the dough into a ball. Wrap in plastic wrap and let stand at room temperature for 30 minutes.
Cut the dough into quarters. Work with one piece at a time and keep the rest wrapped in plastic. Flatten the dough slightly and run it through successively narrower settings on a hand-cranked pasta machine until you reach the last setting. Trim the ends and cut the pasta into 10-inch lengths; loosely roll them up and and cut into 1/2-inch-wide strips. Drape the pasta noodles over a drying rack. Repeat with the remaining 3 pieces of pasta dough.
In a large pot of boiling salted water, cook the pappardelle, stirring, until al dente, about 3 minutes. Drain the pasta and return it to the pot. Add both butters and toss well. Add the stock and grated cheese and toss to coat. Add the fennel fronds, parsley and chives, season with salt and pepper and toss again.
Transfer the pappardelle to bowls and top with a little olive oil and a pinch of tandoori masala. Serve right away.