Step by Step method

1. Step 1.

   Bring 4 quarts water to boil in large pot. Add pasta and 1 tablespoon salt and cook, stirring often, until al dente. Reserve ½ cup cooking water, then drain pasta.

2. Step 2.

   Meanwhile, melt 4 tablespoons butter in 12-inch nonstick skillet over medium heat. Add hazelnuts and sage and cook until sage is crispy, about 3 minutes. Using tongs, transfer sage to paper towel–lined plate; continue to cook butter and hazelnuts until both are browned and fragrant, about 1 minute longer. Transfer to heatproof bowl and stir in vinegar and ⅛ teaspoon salt.

3. Step 3.

   Melt remaining 1 tablespoon butter in now-empty skillet over medium heat. Add shallot, nutmeg, and remaining ½ teaspoon salt and cook, stirring occasionally, until shallot is softened, about 3 minutes. Stir in cream and pumpkin and bring to simmer. Cook until thickened, about 5 minutes. Off heat, stir in Parmesan.

4. Step 4.

   Add pasta and toss to combine. Adjust consistency with reserved cooking water as needed. Serve, topped with sage and hazelnut butter.