Heat a large 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.

Meanwhile, bring a large pot of water to a boil over high heat for the pasta.

To the skillet with the sausage, 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 red 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, cheese rind and rosemary sprig. Reduce the heat and simmer gently for 15 minutes.

Once the pasta water is boiling, season generously with kosher salt. Add the pasta to the water and cook until just al dente, about 8-10 minutes. Reserve 1 cup of pasta water.

Remove and discard the Parmesan rind and rosemary sprig 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.