Set a large pot or Dutch oven over high heat. Sprinkle the short ribs all over with a generous amount of salt and some pepper (no flour required here!). Add the oil to the pot and brown the short ribs well on each of the 3 meaty sides, about 15 minutes total. Work in batches so as to not overcrowd the pot. You want a deep brown color on the meat as this will give the stew its rich flavor and color when braising. Remove the ribs and set aside.
Add the carrots, celery and onions to the pot. Saute the vegetables until caramelized and wilted, 8 to 10 minutes. Add the garlic and toss to combine and heat through. Return the ribs to the pot and nestle in amongst the vegetables. Add the thyme, bay leaves, rosemary, stout beer, broth and tomatoes. Season lightly with salt and pepper, then stir and bring to a boil. Reduce the heat, cover with a lid and simmer the ribs 2 1/2 hours. Periodically skim any excess fat on the surface and discard.
After 2 1/2 hours, mix in the pearl barley and dry mustard powder, then cover once more and cook 45 more minutes. When done, remove the bay leaf, thyme and rosemary stems. Taste and season the braise with salt and pepper and serve.