Put the milk in a large pot over medium-high heat. Cook, stirring often to avoid scorching, just until the milk bubbles around the sides of the pot, 10 to 15 minutes. Line a strainer with 3 layers of cheesecloth. Add the buttermilk to the steaming milk and stir a few times, then turn off the heat and let the mixture sit until it separates into solids (curds) and liquid (whey). Stir in a large pinch of salt.
Carefully ladle the mixture into the prepared strainer. Leave the ricotta in the strainer set over the large pot until much of the whey has drained off, but the cheese is still loose and easy to work with, about 30 minutes. Taste and adjust the seasoning. (At this point you can transfer the ricotta to an airtight container and refrigerate for up to 2 days.) Discard the whey or reserve for another use.
Combine the flour and 1 teaspoon salt in a food processor and pulse once or twice. Add 2 eggs and 3 yolks and turn the machine on. Process just until a ball begins to form, about 30 seconds. Add a few drops of water if the dough is dry and grainy; add a tablespoon of flour if the dough sticks to the side of the bowl. Sprinkle the dough with a little flour and cover; let it rest for about 30 minutes. (At this point, you can refrigerate the dough, tightly wrapped in plastic, for up to 24 hours. Let it sit out for 15 minutes before proceeding.)
Set up your pasta machine and sprinkle the work surface lightly with flour. Cut off about one-third of the dough and wrap the rest in plastic or a dishtowel while you work. Roll the dough lightly in the flour and use your hands to flatten it into a rectangle about the width of the rollers. Set the machine to its thickest setting and roll the dough through. If it sticks, dust it with a little more flour. Repeat. Set the machine to its next-thinnest setting and repeat, putting the dough through each setting twice. Each time, if the pasta sticks, sprinkle it with a little more flour. Continue to roll the dough thinner, changing the thickness only one setting each time (if you try to rush the process, the dough will tear). If at any point the dough tears badly, bunch it together and start again. Use only as much flour as you need to. Pass the dough through the machine’s third-thinnest setting. Repeat 2 more times (by this time it will be going quickly), then flour the dough lightly, and cover. Repeat with the remaining dough.
Heat the oven to 200°F. Bring a large pot of water to a boil and salt it. Beat the remaining whole egg and 1/2 cup water in a small bowl and lightly flour your work surface. Cut as many of the pasta sheets as you need to make sixteen 5-inch squares (keep extra handy).
Bring the ricotta to room temperature if it isn’t already. Mix the ricotta, 1/2 cup Parmesan, and lots of pepper and salt; taste and adjust the seasoning. Transfer to a pastry bag, or a zippered storage bag with one corner cut off to make a 1⁄2-inch opening. Dust a rimmed baking sheet generously with flour.
Brush one pasta sheet with the egg wash almost all the way to the center. Pipe a 2- to 2 1/2-inch ring of ricotta in the center of a pasta square, leaving space for a yolk to fit snuggly inside. Pipe another ring on top. Carefully put 1 egg yolk inside the ricotta ring without breaking. Drape another square of pasta on top, then very carefully press the top sheet onto the bottom, making sure the egg doesn’t spill; it’s okay if the edges don’t line up but there should be no air bubbles or gaps in the seals. Repeat to make 7 more ravioli. Use a sharp knife, or large biscuit cutter or ring mold, to cut the ravioli into 4-inch circles. Discard the scraps and transfer the ravioli to the prepared pan. Refrigerate until ready to use, up to 8 hours.
Put the butter in a large skillet over medium heat. When it melts, add the shallot and cook, stirring occasionally, until the shallot is soft and translucent, 3 to 5 minutes. Remove from the heat, add the herbs, and sprinkle with salt and pepper. Taste and adjust the seasoning. Pour half the sauce into a large baking dish and transfer to the oven.
Lower the ravioli into the boiling water with a spatula 1 or 2 at a time, yolk side up, and boil until it floats, 2 to 3 minutes. Lift out the ravioli with a slotted spoon or strainer and transfer to the baking dish in the oven. Repeat with the remaining ravioli until all have been cooked. Warm the butter sauce remaining in the skillet over low heat and drizzle over the ravioli. Garnish with the remaining 1/2 cup Parmesan and serve right away.