Preheat the oven to 425 degrees F. Cut the butternut squash in half, scoop out the seeds and pulp, and brush with olive oil. Roast, cut-side up, for about an hour, or until tender when pierced with a knife and beginning to brown. When cool enough to handle, scoop the flesh into a food processor and purée until smooth. Place the puree in a small saucepan and cook over medium heat, stirring constantly, until the puré is thickened, about five minutes. (This will remove all extra moisture from the squash.) Set aside one cup of purée for the gnocchi and save the rest for another use.
Meanwhile, boil the potatoes in salted water for about 20 minutes, or until tender when pierced with a knife. Drain the potatoes and press them through a potato ricer into a medium bowl. Measure out two cups of potatoes for the gnocchi. Let cool completely. Measure out the remaining gnocchi ingredients and have lined up ready to go. Prepare two parchment-lined sheet trays.
Using a spatula, gently combine the squash purée, potatoes, 1/2 cup Parmesan, egg, pinch of nutmeg, and salt in a large bowl. Fold in a cup of flour, gradually adding the remaining half cup until a soft, slightly sticky dough forms. Feel free to add a few more tablespoons of flour if necessary, taking care not to overwork the dough.
Turn the dough onto a floured surface and knead several times to form a smooth ball. Using a floured dough cutter (or a sharp floured knife), divide the dough in half. Then cut into fourths, and eighths, sprinkling the dough balls with additional flour.
Working with one dough ball at a time, pat the ball into a small log and begin rolling it into a long rope. The dough should ideally feel sort of like Play-Doh, though mine felt slightly softer. If it becomes too soft to roll, use your hands to stretch the dough and pat it into a long rope about 1/2- to 3/4-inch thick (depending on how big you want your gnocchi to be). Using the dough cutter, cut the rope into 1/2- to 3/4-inch pieces (again, personal preference). Place the little dumplings on the parchment-lined sheet tray and chill for about 30 minutes in the refrigerator. This step wasn’t in the original recipe, but I found it extremely helpful in shaping the dough–if it’s too soft, it’s very difficult to shape the gnocchi.
Remove the dumplings from the fridge and roll them, one by one, over the back of fork tines dipped in flour. Press lightly with your thumb as you roll, and they should have small grooves down one side. Watch the video for clarification! Place the dumplings back on the sheet tray and let chill until ready to boil. Continue the process with the remaining dough balls.
Working in batches, boil the gnocchi in a large pot of salted water until they rise to the surface. Remove them with a slotted spoon onto two parchment-lined sheet trays. I did this in four batches, and each batch took around 3-5 minutes. Let chill until just before dinner.
To make the sage butter, heat two large sauté pans over medium-high heat. Place 1/2 stick of butter in each pan and let melt and begin to brown just slightly, about 2 to 3 minutes. Add the sage and cook for an additional minute. Add half the gnocchi to each pan and sauté until heated through and just beginning to brown, about 5 minutes. Season with salt and pepper and toss with the additional 1/4 cup Parmesan.
Serve the gnocchi with additional grated Parmesan and topped with a fried sage leaf. Buon appetito!