Preheat your oven to 400°F (200°C). Toss the peeled and cubed butternut squash with a drizzle of olive oil and a pinch of salt. Spread evenly on a baking sheet and roast for about 25-30 minutes until tender and caramelized on the edges. Let it cool slightly before transferring to a food processor.
In the food processor, puree the roasted squash until smooth. Transfer to a bowl and mix in ricotta cheese, grated Parmesan, egg, salt, black pepper, and nutmeg. Stir until well combined. Set the filling aside while you prepare the pasta dough.
On a clean surface, mound the flour and create a well in the center. Crack the egg into the well and add olive oil and a pinch of salt. Slowly mix the egg into the flour using your fingers or a fork, gradually incorporating more flour until a dough forms. Knead the dough for about 8-10 minutes until smooth and elastic. Wrap it in plastic wrap and let it rest for at least 30 minutes.
Divide the dough into two portions. Using a rolling pin or pasta machine, roll each portion into thin sheets about 1/16 inch thick. Dust with flour to prevent sticking.
Place small spoonfuls (about 1 teaspoon) of filling spaced evenly on one sheet of pasta. Lightly brush water around each mound to help seal. Carefully lay the second sheet of dough over the top. Press around the filling to seal, making sure to remove any air pockets. Cut into individual ravioli squares using a knife, pizza cutter, or ravioli mold.
Bring a large pot of salted water to a gentle boil. Add the ravioli in batches and cook for 3-4 minutes or until they float to the surface and are tender. Use a slotted spoon to transfer cooked ravioli to a serving dish.
In a skillet, melt the unsalted butter over medium heat. Continue cooking, swirling the pan occasionally, until the butter turns golden brown and smells nutty. Add fresh sage leaves and cook for about 1 minute until crispy and fragrant. Remove from heat.
Drizzle the browned butter sage sauce over the cooked ravioli. Garnish with extra Parmesan cheese and freshly ground black pepper if desired. Serve immediately and enjoy the warm, comforting flavors.
