Allow the beef ribs to sit on the kitchen counter for half an hour to warm them up before searing.
Generously season the beef ribs with 1 teaspoon salt and ½ teaspoon pepper. Preheat the oven to 325 degrees F.
Heat the vegetable oil in a large 6 or 7-quart Dutch oven over high heat until it starts to smoke.
Place the seasoned beef ribs in the Dutch oven, making sure not to overcrowd them. You might have to sear the meat in two separate batches. Sear for 5 minutes on each side until they're nicely browned.
Remove the beef ribs from the Dutch oven and place them on a plate. Reduce the temperature to medium heat and add the celery, carrots, and onion. Cook until the onion is translucent. Season with ½ teaspoon salt and ½ teaspoon pepper
Stir in the tomato paste and Worcestershire sauce and cook until you see the tomato paste has started to stick to the bottom (this caramelization process creates excellent flavor).
Pour in the red wine and scrape up the bits from the bottom of the Dutch oven.
Allow the mixture to come to a boil, and then reduce to medium heat. Add the beef stock, garlic thyme, beef ribs (along with any accumulated juices) to the Dutch oven.
Cover and place the Dutch oven in the oven to cook for 3 hours.
When done, transfer the beef ribs to a plate. Discard the onion, celery, carrots, and thyme sprigs using a slotted spoon.
Return the Dutch oven to the stove and simmer the gravy until reduced by half and thickened.
Place the beef ribs back into the Dutch oven and heat on low until they are warmed through. If you like, season with salt and pepper to taste.
Serve the beef ribs over whipped mashed potatoes and the gravy.