Prepare the dough: Sift flour and salt onto a clean surface. Make a well in the center and add the egg, egg yolks, and oil. Gently whisk the wet ingredients together, gradually incorporating the flour until a dough forms.
Knead the dough: Once the dough is too stiff to mix, use a bench scraper to bring it all together. Knead by hand for 7-10 minutes until smooth, adding more flour as needed. Cover and rest for 30 minutes.
Roll out the dough: Roll the dough into a ¼-inch thick rectangle, then pass it through a pasta roller, gradually decreasing the size setting until thin enough to see through.
Make the filling: In a bowl, combine ricotta, mozzarella, parmesan, pumpkin, garlic, salt, pepper, and nutmeg. Set aside.
Prepare brown butter sauce: Melt butter in a saucepan, add garlic, and cook for 1 minute. Stir in salt, pepper, and sage, then remove from heat.
Assemble ravioli: Lay out pasta sheets, spray lightly with water, and spoon 2 teaspoons of filling onto the dough, leaving 1-inch gaps. Fold the dough over the filling, press to seal, and cut into individual ravioli.
Cook ravioli: Boil salted water, add ravioli in batches, and cook for 3-4 minutes. Strain and plate.
Serve: Drizzle with brown butter sauce, top with parmesan and parsley, and serve immediately.