Bring a large pot of water to a boil. Salt the water and add the butternut squash. Cook until soft, about 12-15 minutes.
While the squash is cooking, fry the sage leaves. Heat 3 tablespoons olive oil in a small skillet over medium-high heat until surface is shimmering slightly. Add a few leaves at a time and cook until crisp, but still bright green, about 30 seconds. Transfer to a paper towel to drain. Season with salt. Set aside.
Using a large slotted spoon, carefully remove the squash from the water and place in a large bowl. Add the pasta to the boiling water and cook according to package instructions.
Place the cooked butternut squash in a large food processor or blender. Puree the squash until smooth. Add water or broth and puree until the sauce reaches your desired consistency. You may need a little more or a little less water depending on the size of your squash.
In a large deep skillet, heat 1 tablespoon of olive oil over medium-high heat. Add onion and garlic and saute until soft, 3-5 minutes. Add pureed butternut squash. Stir in the Parmesan cheese. Season with nutmeg, salt, and pepper. Add the pasta and stir until pasta is well coated. Chop two of the sage leaves and stir them into the pasta. Serve the pasta with remaining fried sage leaves and additional Parmesan cheese, if desired.