Make a mound with the flour, plus a pinch of salt. Then make a well in the middle in which to put the eggs. Beat the eggs with a fork and then slowly use the fork to incorporate the flour. Once the eggs are absorbed, use your hands to knead the dough for 10 minutes until smooth. (Of course, you can use a kitchen mixer with a knead attachment to accomplish the foregoing.) Wrap the dough tightly in plastic and set aside for 20 minutes.
Cut the dough into 4-6 pieces of equal size, but use only one piece at a time (leaving the remaining dough wrapped in plastic). If you are doing this the old fashion way, with a rolling pin, then roll it out, fold it back several times, and continue this process until thin. Alternatively, pass it through a pasta machine until thin (or until it goes through the second thinnest setting at least twice).
Prepare the Filling
Cut the pumpkin vertically into 1 inch strips. Place the strips on a cookie sheet lined with parchment paper, cover with foil, and place in a preheated oven of 400 degrees. Bake for approximately 30 minutes, or until soft. Allow to cool and peel. Mash with a fork and let it cool . In a large mixing bowl, combine the pumpkin, ricotta, Parmigiano, nutmeg, salt and pepper and mix until smooth. Set aside.
Prepare the Ravioli
With a pastry cutter or a glass, cut the sheet of pasta into 3 inch discs. Add a spoonful of the ricotta mixture in the center of each disc and brush the outer edge of the ravioli with a little egg white. Cover with another disc and firmly press the edge to seal the ravioli. Use a fork, if desired, to further seal the edge, or gently fold over. Place the ravioli on a well-floured surface until ready to cook.
Prepare the Sauce
In a large skillet over medium heat, melt the butter and cook for a few minutes until browned.
Bring a large pot of salted water to a boil. Cook the ravioli in salted water until al dente (2-3 minutes or until floating) and remove with a slotted spoon. Place onto a serving plate, and cover with browned butter and a sprinkle of Parmigiano.
Total time is 60 minutes if using pre-made pasta sheets.