Bring a large pot of water to a boil for the pasta.
In a large skillet, heat the olive oil, half a turn of the pan, over medium-high. Add the butter. When it foams, add the sausage and walnuts, and cook, stirring and breaking up the sausage with the back of a spoon until the sausage is cooked through and the mixture is deep golden brown, about 5 minutes.
Add the shallots and garlic, and stir until the shallots soften, 1-2 minutes. Add the prosciutto and rosemary. Stir to heat through, 1-2 minutes. Add the brandy or Vin Santo and stir, scraping up any browned bits on the bottom of the skillet. Add the cream and sage, and bring to a bubble. Reduce the heat to low and let simmer, stirring occasionally, while the pasta cooks.
Salt the boiling water, add the pasta and cook to al dente. Drain, reserving half a mug of cooking water. Toss the pasta and 1 cup cheese into the sauce, adding cooking water as needed to thin the sauce. Serve in shallow bowls, passing more cheese alongside.