To make the stock combine the ingredients and cook over low heat for 1 hour-1.5 hours skimming the foam, which will rise to the surface once in a while. Alternatively, this could be done in Instant Pot, which will cut down the cooking time to 30 minutes on high pressure plus 20-23 for the Instant Pot to come to pressure. Alternatively, skip the first step and use already prepared beef or chicken broth. (See recipe notes at the bottom for instructions.)
Add the pearl barley to a medium pot filled with cold water, bring to a boil, then continue cooking for 10 minutes. Drain and rinse with cold water thoroughly and set aside till needed.
Once the stock is ready, remove the pork ribs from the stock, allow them to cool. Meanwhile strain the stock through a fine sieve and discard the vegetable. Once the ribs are cool enough to handle, remove the meat from the bones, discard visible fat and cartilage, then shred or cut into bite-sized pieces, discard the bones.
Add the strained stock to a soup pot and bring to a simmer, to the same pot add the shredded meat, the partially cooked pearl barley and cubed potatoes with a good pinch of salt and cook for 10 minutes.
While the soup is cooking sauté the chopped onions and diced carrots in 1-2 tbsp of butter for 5 minutes, then add the garlic, diced dill pickles and continue sautéing over low heat for 5 minutes longer, then stir in the tomato paste and scrape the contents of the pan into the soup pot, pour in the pickle brine and cook for 5-10 minutes or until the barley is cooked all the way through.
Once finished cooking add salt and black pepper to taste. Take of the heat, cover with a lid and let it sit for 15 minutes. This will allow the flavour to meld together. Serve sprinkle with fresh dill and parsley.