Heat up the olive oil in a heavy bottomed pot you plan to cook the entire soup. Add the onion, garlic, and celery, and sauté until soft and fragrant, about 10 minutes.
Stir in the tomato paste, turmeric, salt and pepper, and cook for another couple of minutes.
Add the broth, bring to a simmer, and add the potato and cooked barley. Simmer until the potato is tender, about 10 minutes.
Stir in the fresh mint, lime juice, and serve immediately with a crust of bread.