Preheat the oven to 350℉ with the rack in the center position.
Season the pork all over with salt. Heat the oil in a large Dutch oven over high heat. Once the oil is glistening, add the pork in batches and cook until browned all over, about 15 minutes total. Transfer the pork to a plate. Discard half of the fat from the pot, then return it to medium heat.
Add the onion, carrots, and celery. Cook, stirring occasionally, until beginning to soften, about 4 minutes.
Add the garlic and cook for 1 more minute, until fragrant.
Stir in the tomato paste until evenly coated. Add the tomato sauce and white wine, stirring to combine. Increase the heat to high and bring the sauce to a simmer.
Return the pork to the pot, nestling it into the sauce and adding any collected juices.
Tie the thyme, basil, parsley, and sage together using cooking twine. Add the herbs to the pot.
Cover, transfer to the oven, and cook for 3 to 3½ hours, until the pork is very tender and falling apart.
Discard the herbs. Using tongs or two forks, transfer the pork to a cutting board and shred it, discarding any large pieces of fat.
Return the shredded pork to the pot and stir to incorporate. Season with salt and black pepper to taste.
Serve the ragù over pappardelle or polenta.