Roast the pork and the chicken—see Kitchen Notes.
In a big, heavy pot, heat the butter, lard and oil. Then put in the kielbasa coins and quickly brown on both sides. Set aside. If need be, add a bit more oil to the pot and scrape the bottom. Then add the onions and sauté for a minute or two, until translucent. Add the tomato paste and sauté some more, stirring, two or three minutes.
Then add the drained sauerkraut, the stock, the shredded cabbage, the spices and the bay leaves, and stir everything together. When it is all uniform, add the grated apple, the chopped prunes, and the fresh and dried mushrooms. Stir in the meat. Bring to a simmer, then cook gently over low heat for a couple of hours, uncovered, stirring now and then.
Taste part way through—if it tastes sour, then add more apple or prune. After about two hours, turn off the heat. You may serve it right away, as noted above, but for maximum awesomeness, put it away in the fridge overnight, then cook a bit more the next day.
We served this with a baguette and plenty of butter and, to drink, a terrific 2017 Averaen pinot noir from Oregon's Willamette Valley that our friends Chris and Julie brought. Its light style is perfect for bigos. Or, of course, a good Polish beer.