Heat the olive oil over medium-high heat in a large skillet or Dutch oven.
Sprinkle the duck legs with salt and pepper. Sear in the hot pan until golden brown and crisp, 10 minutes. Remove to a plate.
Add the carrots, celery and onions, and saute until soft, 3 minutes. Add the thyme and garlic, and saute until fragrant, 1 minute.
Add the red wine. Use the back of a wooden spoon to scrape up the browned bits from the duck; this will add to the flavor of the finished sauce. Cook for 2 minutes, then stir in the tomatoes, some salt and pepper and bring to a gentle simmer. Add the seared duck back to the pan and cover. Simmer gently until the duck is extremely tender and falling off the bone, 1 hour and 30 minutes.
Remove to a casserole dish to cool. Remove the skin and bones and discard. Chop the meat finely and add it back into the tomato sauce, adding a half a cup of water if it looks dry, and simmer, covered for 40 minutes.
Serve over Homemade Pappardelle. Drizzle with extra-virgin olive oil serve with freshly grated Parmesan and parsley.
To make the pappardelle:
Add the flour and salt to the center of a large wooden board. Use your hands and make a well in the center of the mound. Whisk together the eggs and olive oil in a bowl and pour into the well. Use a fork to whisk the eggs into the flour, incorporating slowly into the rim of the flour until it is completely incorporated.
Once incorporated, knead the pasta for about 8 minutes, adding just a bit more flour if the board is sticky. If the dough feels too dry, add a drop of water as you go. The dough should feel elastic, smooth and a bit sticky. Shape the pasta dough into a ball and wrap in cling film. Let rest for at least 30 minutes to 1 hour at room temperature to let the gluten relax so rolling will be easier.
Set your pasta machine to the widest setting. Divide the dough into 4 pieces. Roll each piece out from the widest setting to the thinnest. Hand cut the pasta into pappardelle.
Gather the strands together in your hands and shake loosely so they don't stick together. Toss with some semolina flour. Divide into portions on a sheet tray.
Bring a pot of salted water to boil. Boil the pasta until al dente and drain, about 3 minutes.