Heat the vegetable oil in a large pot over medium heat.
Add the pork pieces and cook until browned on all sides. Remove the pork and set aside.
In the same pot, add the chopped onion and cook until soft and translucent, about 5 minutes.
Stir in the minced garlic and cook for another minute.
Add the drained sauerkraut and pearl barley to the pot. Stir to combine.
Return the browned pork to the pot.
Pour in the chicken or vegetable broth, add the caraway seeds and bay leaf, and stir to combine. Bring to a boil.
Reduce heat to low and simmer for 40-50 minutes, or until the barley is tender and the pork is cooked through.
Season with salt and black pepper to taste.
Garnish with fresh dill before serving.
Enjoy your meal!