3/4 cup mixed torn herbs such as mint, basil, and Italian parsley, divided
2 cups whole-wheat flour
1 cup semolina flour, plus more for dusting
4 large eggs
4 large egg yolks
Place a heavy pan or braiser over medium-high heat. While it heats, use a paper towel to dry the lamb shanks well, drizzle them with 1 teaspoon of the oil, and season them evenly with 1 teaspoon of the salt and the black pepper. Add 1 tablespoon oil to the pan and heat another 20 seconds. Add the lamb shanks to the pan and cook, turning occasionally, until evenly browned on all sides, about 12 minutes. Transfer the lamb to a plate.
To the hot pan add the remaining 1 tablespoon oil, the onions, carrot, celery, and remaining 1 teaspoon salt. Cook, stirring often with a wooden spoon and scraping the brown bits from the bottom of the pan, until the vegetables begin to soften, about 5 minutes. Add the garlic and rosemary and cook until fragrant, about 2 minutes more. Add the tomato paste and cook, stirring often, until the paste is slightly darker in color and smells sweet, about 2 minutes longer.
Add the wine and simmer until the pan is almost dry. Stir in the tomatoes and crush them with the back of a spoon. Add the stock and bring to a simmer. Reduce the heat to medium-low to maintain a gentle simmer. Nestle the lamb shanks back into the liquid, cover the pan with a lid and simmer until the lamb is tender, 2 1/2 to 3 hours, checking occasionally to make sure the liquid is at just a simmer.
When tender, transfer the shanks to a plate. Use 2 forks to pull the meat from the bones and shred the meat into bite-size pieces. Knock or scoop the marrow out of the bones and add the marrow and the meat back to the sauce. Discard the bones.
Continue to simmer the sauce, uncovered, until it has thickened slightly, another 20 to 30 minutes. Taste the sauce and season with more salt if needed. Remove 2 cups of sauce for another use or freeze for later. Keep the remaining sauce warm.
Bring a large pot of water to a boil. Season generously with salt. Add the whole-wheat pappardelle to the water and stir immediately to prevent sticking. Cook until just barely al dente, about 1 1/2 minutes. Using tongs and a pasta spider, remove the pasta from the water and add directly to the sauce; reserve the cooking water. Toss the pasta in the sauce, adding up to 3/4 cup of pasta water as needed.
Remove from the heat and add the butter and egg yolks and sprinkle in 1/2 cup of the Parmesan cheese. Immediately toss again to combine until the sauce is creamy and coats the pasta. Toss in 1/2 cup of the herbs. Serve with the remaining 1/2 cup parmesan Parmesan cheese and the remaining 1/4 cup herbs.
Spoon the whole-wheat flour and semolina flour onto a board. Use your fingers to mix the two flours together and make a well in the center. To the center of the well add the whole eggs and egg yolks. Use a fork to whisk the eggs together until smooth. Slowly start incorporating the flour into the egg mixture until a shaggy dough forms; be careful not to break the walls of the well.
Start kneading by gathering the shaggy dough up and then pushing it away with the heel of your hand. Continue this kneading motion until the dough is smooth and supple; it may take up to 10 minutes. The dough is ready when it springs back slightly when pressed. Form the dough into a smooth disk and wrap in plastic wrap. Allow the dough to rest in the refrigerator for at least 1 hour and up to 1 day.
Cut the dough into 4 pieces. Prepare a pasta machine according to the manufacturer’s instructions and set it to its thickest setting. Using the heel of your hand, flatten a piece of dough to about 1/3-inch thick. Feed the dough through the pasta roller. Fold the pasta in thirds and put it through the roller again on the same setting. Repeat this process one more time on that setting. Continue to roll out the dough, reducing the setting on the roller until the desired thickness is reached, about 1/8 inch, approximately setting 5 depending on your machine.
Dust the pasta sheet with semolina flour. Fold the dough half and use a pizza wheel or a knife to cut the dough into 3/4-inch-wide strips. Unfold the pasta and place the strands on a rimmed baking sheet and dust with semolina flour to prevent sticking. Repeat with the remaining dough. If not using it right away, refrigerate the pasta uncovered until ready to use.