Brown the meats: Heat 1 tablespoon of oil or lard in a large pot. Brown the pork shoulder, beef stew meat, and kielbasa sausage in batches, removing them from the pot as they brown. In the same pot, cook the chopped bacon until crispy. Set the meats and bacon aside.

1. Sauté the vegetables: Add more oil to the pot if needed and sauté the onion and garlic until softened, about 5 minutes.
2. Add the cabbage and sauerkraut: Stir in the fresh cabbage and cook for 5 minutes. Add sauerkraut and dried mushrooms (if using), and cook for an additional 3-5 minutes.
3. Combine the ingredients: Return the browned meats and bacon to the pot. Stir in the tomato paste, beef broth, red wine, bay leaves, thyme, black pepper, and sugar (if using). Add more water or broth if needed to cover the ingredients.
4. Simmer the Bigos: Bring the stew to a simmer, reduce the heat, and cook for 1.5-2 hours, stirring occasionally. If you prefer, let it simmer for a few extra hours to deepen the flavors.
5. Taste and adjust seasoning: Once cooked, taste the Bigos and adjust the seasoning with salt and pepper as needed. Add sugar to balance acidity if desired. Remove the bay leaves before serving.
6. Serve: Garnish with fresh parsley and serve hot with crusty bread or potatoes.