01 - Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente. Reserve 1/2 cup pasta cooking water, then drain using a colander.
02 - While pasta is cooking, heat olive oil in a small skillet over medium heat. Add the chopped walnuts and cook, stirring regularly, for 3 to 4 minutes until golden and fragrant. Transfer to a plate and set aside.
03 - In a large skillet, melt unsalted butter with olive oil over medium heat. Add minced garlic and chopped sage; sauté for 1 to 2 minutes until aromatic.
04 - Stir in pumpkin puree, heavy cream, nutmeg, salt, and black pepper. Cook gently for 3 to 4 minutes, stirring occasionally to combine.
05 - Add grated Parmesan cheese to the skillet and stir until melted and smooth. If the sauce is too thick, blend in reserved pasta cooking water a little at a time until desired consistency is reached.
06 - Add drained pasta directly to the skillet with sauce and toss until evenly coated. Cook for 1 to 2 minutes until heated through.
07 - Transfer pasta to serving plates and top with toasted walnuts, extra Parmesan cheese, and fresh sage leaves if desired. Serve immediately.