Rinse the ribs and pat them dry. Trim off any visible fat and cut them into 1 or 2 rib sections.
Place the ribs in the Instant Pot along with the leek, carrot, celery root, allspice, peppercorns, and bay leaves. Cover with water, then lock the lid and set on high pressure for 1 hour.
Meanwhile, dice the onion and potatoes. Using a box grater, grate the pickles length wise over a medium bowl.
Melt the butter or ghee in a large skillet over medium heat. Add the onion and cook until it is translucent, about 7-8 minutes.
Squeeze out the grated pickles, reserving the brine, and add them to the skillet. Cook until the pickles start to turn golden brown, about 5- 6 minutes, then remove the saucepan from heat.
When the Instant pot timer goes off, allow the pressure to naturally release, then unlock the lid. Strain the broth, reserving the pork and carrots, then return broth to the pot. Set the Instant pot to the "Sauté-High" setting.
When the broth comes to a boil, add the potatoes, and loosely cover with the lid. Cook until the potatoes are tender, about 12-15 minutes.
When the ribs have cooled, remove the meat from the bones, shred it and add it to the Instant pot. Grate or roughly chop the carrots and add them to the pot.
Stir in the pickle and onions mixture into the Instant Pot and add the fresh dill. Pour in the reserved juice from the grated pickles, then gradually add the brine from the pickle jar, about a cup at a time, to taste.
Ladle the soup into bowls and garnish with more fresh dill.