Heat the oil in a large, heavy-bottomed pot until it is shimmering and just starting to smoke. Toss the pork with salt and pepper and brown thoroughly in small batches. If you crowd the pan you won’t get the deep colour you need. Remove and set aside.
If there is more than 2 tbsp. of fat in the pot discard some of it. If less than that amount add a little more oil.
Add celery, onion and mushrooms to pot and cook over high heat, stirring, until the mushrooms release their moisture, it evaporates and everything starts to brown. Make sure you scrape up every little bit of flavour from the bottom of the pot as the liquid comes out of the vegetables. Add the garlic and cook another minute, until it is fragrant. Sprinkle in the flour and cook, stirring, until everything is evenly coated.
Add wine or water and let it sputter and mostly evaporate. Return the meat to the pot and add the broth, thyme and bay leaves. Bring to a boil, reduce heat, cover and simmer for 45 minutes, until the meat is tender.
Add potatoes carrots and cook 20 minutes, until both are tender but not falling apart. Add the Brussels sprouts and simmer just until cooked, another 5 minutes or so.
Fish out and discard the thyme stalks and bay leaves. Add salt and pepper to taste just before serving.