Place the butter in a medium pot (with a lid) over medium heat. Let melt, then add the olive oil and walnuts. Cook until the walnuts are lightly toasted and the butter is golden brown, 2 to 3 minutes. Use a slotted spoon to transfer the walnuts to a paper towel lined plate.

Add the garlic and sage to the pot and cook briefly until golden and aromatic, about 1 minute. Add the squash, broth, salt and pepper. Bring to a simmer, then cover and cook for 15 to 20 minutes, or until the squash is fork tender.

Transfer the squash mixture to a blender. Cover, then remove the top insert from the lid and cover with a kitchen towel (to let steam escape). Puree until very smooth, about 1 minute.

Meanwhile, bring a large pot of water to a boil. Season with salt. Add the pasta and reduce to medium heat (just simmering). Cook 1 minute less than the package directions. Reserve ½ cup of the pasta water then drain the pasta in a colander.

Return the large pot to medium heat. Add the butternut squash sauce, heavy cream, cooked pasta and ¼ cup of the pasta water and parmesan cheese. Stir gently with a rubber spatula, until the sauce has thickened slightly and is coating the pasta, about 2 minutes. (Add more pasta water to reach desired consistency). Season with more salt and pepper to taste.

Serve immediately topped with more chopped sage, parmesan cheese, and the reserved walnuts.