In a bowl, mix together the pumpkin puree, ricotta cheese, grated Parmesan, nutmeg, salt, and pepper until well combined.
Lay out the fresh ravioli on a clean surface. Spoon a small amount of the pumpkin mixture onto half of the ravioli.
Top each filled ravioli with another piece of ravioli and press the edges together to seal.
Bring a large pot of salted water to a boil. Cook the ravioli according to the package instructions until they float to the top, usually about 2-3 minutes.
In a separate pan, melt the butter over medium heat. Add the fresh sage leaves and cook until the butter begins to brown slightly.
Remove the cooked ravioli from the pot with a slotted spoon and transfer them to the pan with the browned butter and sage.
Gently toss the ravioli in the butter sauce until coated.
Serve the ravioli hot, garnished with additional grated Parmesan cheese.