Preheat the oven to 325 degrees.
Cut the pork shoulder or butt into 3 or 4 pieces that will fit into your pot. Bot the meat dry with a paper towel.
Heat a large (4 qt) heavy bottom lidded dutch oven or pot over medium-high heat.
Add the olive oil and swirl to coat the pan. Add the meat.
Let the meat cook for about 5 minutes or until the bottom is nicely browned and easily lifts off the bottom of the pan. If the meat sticks, it's not done searing yet!
Flip the meat over and sear the other side.
Remove the meat from the pan and add the onions, garlic and celery.
Cook, stirring often for another 4 - 5 minutes or until the onion is translucent and the vegetables are tender.
Add the salt, pepper, herbs and stir for another minute.
Add the tomato paste. Stirring constantly for 3 - 4 minutes until the tomato paste is a dark reddish brown. Tomato paste can burn, so keep stirring!
Add the wine and stir, scraping up the bottom of the pot with a spatula. Cook until the wine is reduced by half, about 5 minutes.
Add the tomatoes and their juices to the pot and stir. Add the meat. If the sauce doesn't cover the meat (it probably won't) spread some of the sauce on top of the meat.
Cover the pan and place in the oven. Bake for approximately 2 hours or until the pork is very tender.
Remove the pan from the oven. Remove the pork and, using two forks, shred the pork meat.
Degrease the sauce by spooning the fat off the top. NOTE: If you refrigerate the sauce overnight, the fat will rise to the top and harden making it very easy to remove.
Add the shredded pork back to the degreased sauce and stir to combine. Serve over the parmesan polenta, passing additional parmesan if desired.