Heat a large straight-sided skillet over medium-high heat. Add the oil and sausage and cook, stirring often and breaking apart the sausage with the back of a wooden spoon, until beginning to brown, about 7 minutes. Add the onion, carrot and 1/2 teaspoon salt. Cook, stirring often, until fragrant and the vegetables are almost cooked through, about 4 minutes. Deglaze with the wine, scraping up the brown bits from the bottom of the skillet. Reduce the heat to medium and simmer until reduced by half, about 3 minutes. Stir in the tomato puree and cheese rind. Reduce the heat and simmer gently for 15 minutes.
Meanwhile, bring a large pot of water to a boil over high heat. Season the water generously with salt. Add the Pappardelle and cook until the pasta is floating and barely al dente, 2 to 3 minutes. Reserve 1 cup pasta water, then drain well.
Remove and discard the Parmesan rind from the sauce. Add the pasta to the sauce and sprinkle the bare pasta with the Parmesan cheese and basil. Add 1/2 cup pasta water and toss well to coat, adding more pasta water as needed to maintain a light sauce. Serve with more Parmesan cheese on top if desired.
In a large bowl, combine the 00 and semolina flours and salt and form a well. Add the egg and yolks to the center of the well. Using a fork, slowly start to incorporate the flour into the eggs to form a rough dough. You may add a splash of water if the dough is too dry or a dusting of flour if it is too wet.
Lightly flour a smooth work surface and pour the dough onto the flour. Knead the dough until it springs back when you press a finger into it, 10 to 12 minutes. Flatten the dough into an even square. Wrap the dough well in plastic wrap and allow to rest for 1 hour at room temperature.
Cut the dough into 3 pieces. Set up a pasta roller according to the manufacturer's directions and set it at the widest setting. Dust one section of the dough with semolina flour and press firmly to flatten the dough to 1/4 inch. Roll the dough through the machine on the widest setting. Fold the pasta dough in thirds and dust the outside with flour. Send it through the widest setting again. Reduce the setting to the next setting. Send the dough through the machine. Fold it in thirds once again and send through the setting one more time. Continue sending the dough through the machine, reducing the setting each time, until the desired thickness is reached, about 1/8 inch. Lay the sheet out on the counter and dust with flour. Use a knife or pizza cutter to cut strips 1 inch by 10 inches. Dust the strips with more flour. Continue with the remaining dough.