This soup freezes especially well so be sure to save the leftovers for a rainy day. Slideshow: More Russian Recipes
In a large heavy pot, heat the oil over medium high heat until hot. Season the pork with 3/4 teaspoon salt and 1/2 teaspoon pepper, then brown on all sides, about 8 minutes total. Transfer the pork to a plate.
Stir the onion into the pot and cook, scrapping up any browned bits, until golden, about 6 minutes. Stir in the chicken stock, sauerkraut, carrot, and reserved pork with any accumulated juices. Simmer the soup, covered, until the pork is tender, about 2 hours. Coarsely shred the pork and season the soup with salt and pepper to taste. Serve the soup sprinkled with the parsley.