In a large pot or Dutch oven, heat the vegetable oil over medium heat. Add the chopped onions and sauté until they become translucent (about 5 minutes).
Add the minced garlic and continue to cook for another minute until fragrant.
Stir in the diced beef chuck and cook until browned on all sides (approximately 6-7 minutes).
Add the sliced smoked sausage to the pot and cook for an additional 5 minutes, allowing it to release its flavors.
Incorporate the grated carrots and tomato paste into the mixture, stirring well to combine.
Add the chopped green cabbage and sauerkraut to the pot, mixing everything together.
Pour in the broth and add the bay leaves, thyme, caraway seeds, salt, and pepper.
Bring the mixture to a gentle simmer, then cover the pot and reduce the heat to low. Let it cook for about 1.5 to 2 hours, stirring occasionally.
Taste and adjust the seasoning if necessary before serving.
Notes
Serve the Bigos in deep bowls garnished with freshly chopped parsley. Consider offering crusty bread on the side for dipping.