Preheat the oven to 325˚F. In a Dutch oven over medium heat, warm 1 tablespoon of the olive oil. Cut the pork shoulder into four equal pieces and season all over with salt and pepper. Use tongs to lower the pork into the hot oil; sear until brown all over, about 3 minutes per side. Remove pork and set aside in a bowl, reserving any juices.
Add remaining 1 ½ tablespoons olive oil to the Dutch oven. Add onion, carrot and celery and sauté until the onions begin to sweat and become slightly translucent, about 5 minutes. Add garlic and season with salt and pepper. Stir together.
Add herbs and continue to sauté for 1 minute until herby and aromatic.
Add tomato paste and stir together. Lightly season with salt and pepper.
Deglaze with wine, making sure to scrape with a wooden spoon along the bottom to release any browned bits. Simmer until ½ of the wine has evaporated, then add the whole tomatoes, including juices, and stir together.
Once mixture is simmering again, return the pork and the juices back into the pot and bring to a boil. Cover pot and transfer to the oven to braise until fork tender, about 2 hours.
Remove pot from the oven and finely shred the pork with two forks. Adjust seasonings if needed. Cover until ready to use.
Fill a large pot with water and place over high heat to bring to a boil. Season generously with a handful of salt. Add the pasta, stirring occasionally, and cook until al dente. Drain.
Divide pasta into individual bowls and top with a large ladle of ragu. Top with freshly grated Parmesan or Pecorino Romano and serve.
Notes
Gluten Free: This ragu contains no gluten if you leave out the egg noodles. Feel free to substitute your favorite gluten-free pasta or serve with mashed potatoes.Egg Noodles: I encourage you to see the instructions in this post about making fresh egg noodles. They are divine. That said, you can find dried egg noodles in the pasta aisle.