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
In a large bowl, combine the mozzarella, ricotta, Parmigiano, parsley, salt, and pepper. Mix well until smooth. Set aside.
Prepare the Sauce
In a large skillet, sauté the onion in the olive oil until golden. Add the tomatoes, salt, and pepper. Cook over medium heat for about 10 to 15 minutes, until slightly reduced.
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.
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 sauce and a sprinkle of Parmigiano.
Total time is 60 minutes if using pre-made pasta sheets.