In a large pot, heat the vegetable oil over medium heat. Add the chopped onion and garlic, and cook until the onion is translucent.
Add the bay leaves, dried thyme, and caraway seeds. Stir to combine.
Pour in the chicken or vegetable broth and bring to a boil.
Add the diced potatoes and cook until they are tender, about 10-15 minutes.
Stir in the kielbasa and cook for an additional 5 minutes.
Reduce the heat to low and stir in the sour rye starter (żur). Simmer for 5-10 minutes, allowing the flavors to meld.
Add the heavy cream and stir well. Season with salt and black pepper to taste.
Remove the bay leaves before serving.
Ladle the soup into bowls. Garnish with fresh dill and serve with hard-boiled eggs if desired.
Enjoy your meal!