Add the 2 tablespoons olive oil to a large enameled cast iron dutch oven and warm over high heat. While the oil heats, season the pork well on all sides with kosher salt and ground black pepper. When the oil is shimmering, add half the pork to the dutch oven and brown on all sides, about 10 minutes. Remove the first batch of browned pork and set aside on a plate, and repeat with the second batch. Keep the pork set aside for later.
Reduce the heat to medium and add the onion, carrots, celery, and pancetta to the same dutch oven. Cook, stirring occasionally, until the pancetta is crispy and the vegetables have a nice golden brown color to them. Don't skimp on this step, since it is the base of the flavor of the dish. You want some dark bits on the bottom of the pan that you'll stir up later when you add liquid.
Meanwhile, preheat the oven to 300 degrees Fahrenheit.
Next, add the garlic and tomato paste to the dutch oven and cook for about 1-2 minutes, until the garlic is fragrant. Pour in the red wine and cook for about 10-15 minutes, or until the wine is mostly evaporated.
Add the 2 cans of tomatoes, including the sauce in the cans. Use a spatula to break up the tomatoes in the pot. Add the fresh thyme, oregano, bay leaves, and 2 cups of beef stock. Use tongs to nestle the pork pieces back into the dutch oven so they are fully submerged in the liquid, adding any accumulated juices to the dutch oven as well. Increase the heat to high and bring everything to a simmer.
Remove from the heat, partially cover the dutch oven with the lid, and place in the oven. Let braise for about 3 hours, until the pork is fall apart tender.
About 30 minutes before you're ready to eat, start cooking the pasta. You'll probably have to cook it in 2 batches unless you have a ginormous pot available. To cook it, bring a large pot of salted water to a boil and cook the pasta according to package directions (time will vary, depending on whether you bought fresh or dried pasta). When the first batch is done, drain the noodles and toss with a little bit of extra virgin olive oil to prevent the noodles from sticking together while the 2nd batch cooks. When the second batch is done, drain, toss with a little bit of olive oil, and add to the first batch.
When the ragu is done braising, remove the dutch oven from the oven and set on the stove. Use a spoon and/or a pair of forks to shred all of the pork pieces into fine shreds and stir the sauce until evenly combined. Stir in a splash of balsamic vinegar, 1-2 tablespoons total, and another 1/2 cup of red wine. If the ragu is a little too thick, add more beef broth to thin to the consistency you desire (although this should be a thick sauce that will stand up to the thick pappardelle noodles and coat them well).
When ready to serve, add noodles to your bowl, top with a generous amount of ragu, drizzle with high quality extra virgin olive oil, sprinkle with flaky maldon sea salt, and top with parmesan/romano cheese and a bit of fresh basil. Enjoy!