Heat a large straight-sided skillet over medium-high heat.
Add the oil and turkey 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.