Tie the roast together with kitchen rope to keep it from falling apart and to guarantee uniform cooking. Season the pork with salt and pepper to taste.
In a big, heavy saucepan, heat the olive oil over medium heat. Add the pork shoulder when the oil is heated but not smoking.
Cook for about 3 minutes, or until golden. When a crust forms on the outside of the pot, the meat will come loose. Give it another minute if it's difficult to lift and clinging to the pot.
Cook for 3 minutes on each side after turning the pork a quarter turn. Repeat with the remaining two sides until all sides are browned.
Remove the saucepan from the heat. Remove the pork roast from the cooker and set it on a big dish or pan. Cover loosely with aluminum foil.
Do not clean the pot. Return it to medium heat. Mix in the onions and celery. Cook for about 2-3 minutes, stirring regularly.
Add the garlic and tomato paste to the saucepan next. Cook for 1 minute, stirring often, while stirring thoroughly.
Stir in the white wine while carefully scraping any particles from the bottom of the saucepan. Cook until most of the wine has evaporated, about 1-2 minutes.
Return the pork roast, along with any juices that have accumulated on the pan, to the pot. Add enough chicken broth to cover the thickest section of the roast 14 times.
Then, surround the roast with potatoes, carrots, rosemary, thyme, and bay leaf.
Increase the heat to medium-high and bring the broth to a simmer. Reduce the heat to medium-low and cover the pan.
Cook for about 3 hours, or until the meat is soft. When a fork is inserted and twisted, it should readily yield and rip.
Keep the liquid at a simmer throughout the cooking period. Reduce the heat if it's boiling too quickly. If it's not simmering, turn it up. Check on it every 12 hours or so, especially after adjusting the heat.
Remove and discard the rosemary, thyme, and bay leaf stems. Serve the roast alongside the carrots and potatoes, as well as rice, crusty bread, Texas toast, or your favorite side dish.