Mound 3 1/2 cups of the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add the eggs and the olive oil. Using a fork, beat together the eggs and oil and begin to incorporate the flour, starting with the inner rim of the well.
As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough with both hands, using the palms of your hands. Once you have a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Roll or shape as desired.
In a heavy 6 to 8-quart saucepan, heat the olive oil until smoking. Add the onion, carrot and celery and cook until softened and light brown (about 12 to 15 minutes). Add the anchovy paste, chili flakes, rosemary, red wine and tomato sauce and bring to a boil. Season the meat with salt and pepper and drop into the tomato sauce mixture. Return to a boil and lower to simmer and cook 90 minutes. The meat should be falling apart with the poke of a fork. Allow to cool 10 minutes. In a food processor, barely pulse 4-ounce ladles of meat mixture until "stew" resembles meat sauce. Check for seasoning and set aside.
Bring 6 quarts of water to a boil and add 2 tablespoons salt.
Place the ragu in a saucepan and bring to a boil.
Drop the pappardelle into the boiling water and cook until tender yet firm. Drain the pasta in a colander over the sink and pour into the ragu. Toss gently to coat and pour into a warm serving bowl and serve immediately.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt and serve. This sauce holds 1 week in the refrigerator or up to 6 months in the freezer. Yield: 4 cups