For the pasta: 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, olive oil and sangiovese. Using a fork, beat together the eggs, oil and wine 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 your palms. Once you've formed a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly re-flour the board and continue kneading for six more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic wrap and allow to rest for 30 minutes at room temperature. Roll or shape as desired.
For the ragu: heat olive oil in a heavy saucepan over medium heat. Season wild boar with salt and pepper then add to the hot oil. Allow boar to brown evenly, taking care not to let the oil burn (around 10-15 minutes). Remove boar from the pan and set aside. Drain any excess fat from the pan then add onion, celery, carrot and garlic. Allow vegetables to cook until soft, about 10 minutes. Add chili flakes then deglaze pan with wine.
Return the boar to the pan and allow to cook until the wine is almost completely reduced. Add tomato and allow ragu to gently simmer for an hour to an hour and a half, or until completely tender.
When you're ready to serve, 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, then pour into a warm serving bowl. Finish with grated pecorino cheese and serve immediately.