Preheat oven to 325 degrees F. Season ribs with salt and pepper on both sides. Be generous with the salt.
In a large Dutch oven heat oil over medium high heat. Working in 2 or 3 batches, brown ribs on all sides creating a nice deep colour. This will take 15 to 20 minutes. Try not to over crowd the pan. This will cause steaming instead of searing which will prevent the meat from browning.
Transfer to a dish and set aside. Remove all but about 2-3 tablespoon of the oil left in the pot.
Lower heat to medium low and add onions, carrots, celery, and garlic. Sautee, stirring frequently, until vegetables start to soften and brown. 5-7 minutes. Add tomato paste and sprinkle with flour. Stir constantly until well combined and a deep red colour, 2-3 minutes.
Add the wine and stir, scraping up all the bits that have stuck to the bottom of the pan. Pour in the stock and stir to combine.
Add ribs and any accumulated juices, making sure the meat is mostly submerged in the liquid. You can add a bit more wine or stock if necessary. Bring to a boil.
Add thyme, bay leaves, and parsley stems. Cover and place in preheated oven for 2 ½ hours or until meat is falling off the bone. This cooking time will vary depending on how big or small the ribs are.
Remove ribs, and any meat that has fallen off, from the sauce and set aside. Skim any fat from the top with a spoon. Strain the sauce, pressing the vegetables to extract all the flavour. Taste and add salt and pepper if needed.
Serve ribs with the sauce on a bed of mashed potatoes, cauliflower mash, or with crusty bread.