Rinse the sauerkraut: Place sauerkraut in a colander, give it a quick rinse under cold water, and drain well.
Brown the pork: In a large pot, melt 1 tablespoon of bacon fat over medium heat. Add chopped pork and brown until golden on all sides.
Add celery and onion: Stir in the celery and onion. Season lightly with salt and pepper. Cook until onions are soft and translucent, adding more bacon fat if needed.
Combine everything: Add sauerkraut, kielbasa, and allspice to the pot. Stir well, then add another tablespoon of bacon fat and mix thoroughly.
Braise low and slow: Reduce heat to medium-low and cook for 3–4 hours, stirring every 20–30 minutes and scraping the bottom of the pot. If it’s browning too fast, reduce heat and add a little bacon fat or broth.
Serve: Once the kapusta is soft, golden, and fragrant, serve warm with mashed potatoes, bread, or pierogi.