Heat the olive oil in a large pot with a matching lid over medium heat. Once hot, add the chopped carrots, onions, and celery and cook for around 5 minutes, or when onions are translucent.
Add the garlic and cook for another minute.
Add beef ribs and pour in the water and broth. Add more water if needed to cover everything.
Add the bay leaf, thyme, and rosemary—season to taste with salt and pepper.
Cover the pot with the lid and bring to a boil. Reduce heat and let simmer until meat is tender (it should be able to fall apart). This should take around 1 hour and a half. Add more broth if needed.
Remove the ribs, bay leaf, thyme, and rosemary from the pot. Shred the ribs with a fork and discard the rosemary and thyme.
Return to the pot and pour in the red wine and barley. Simmer until barley is tender for around 1 hour—season with more salt and pepper to taste if needed.