Kapusta! (When Kimchi will just not do... for your Polish friends)
Kapusta [kah-POOS-tah], the Russian, Hungarian, Polish, Ukrainian, and Slovak word for cabbage, is a popular dish in Polish and Slovak cooking. Its primary ingredient has been pickled into sauerkraut and, in some places, kapusta simply refers to this plain sauerkraut. But in many other homes, this base is frequently amplified with a mix of mushrooms and onions, and that is what is meant by the term kapusta. Some cooks also add meat (usually pork, either rib meat or bacon, or smoked kielbasa), resulting in what is often called bigos. (from Wikpedia)
In some homes, kapusta is served very thin, almost like a soup. In others, its ingredients are cooked until it becomes nearly as thick as mashed potatoes. Kapusta is less ubiquitous in Polish cooking than kimchi is in Korean cuisine, but both serve a similar role in adding bulk to the meal and a background flavour with which other foods contrast.)
One-half firm, fresh head of cabbage, sliced +/- 1/4 inch (Size of cut is very optional to personal taste; but not too thin to cause it to disappear. )
2-3 carrots, peeled and grated coarse
1 medium-large onion, thin 1/2 slices
1-2 apples, crisp variety, cut into medium dice
2T vinegar or to taste
3T sugar or to taste
Salt and pepper to taste
Braise 1 hour with small amount of water
Braising liquid: water with small amount of white wine/marsala/cooking sherry, chicken broth, miso broth***
2 large potatoes, medium cubed (will melt a bit and thicken the dish)
Fresh Mushrooms, sliced
Polish dried mushrooms
Meats: Kielbasa and/or other smoked or fresh sausages; and/or other smoked pork cuts (bacon, ribs, hock, picnic ham)
1-2 T barley (nice textural element, plus thickens dish)
***Miso??? Yes. But maybe then, omit polish type mushrooms and meats. Cook more to soup consistency. Add tofu, garnish with thin sliced scallions. Maybe even add some daikon cubes. Dried Asian mushrooms.(Kapusta Orientale!)
For further inspiration, moving perhaps westward to France/Germany:
(From Wikipedia: Choucroute garnie (French for dressed sauerkraut; choucroute is a phonologically francophonic form of Alsatian Sürkrüt, c.f. German Sauerkraut) is a famous Alsatian recipe for preparing sauerkraut with sausages and other salted meats and charcuterie, and often potatoes.
Although sauerkraut is a traditionally German and Eastern European dish, the French annexation of Alsace and Lorraine following the Peace of Westphalia in 1648 brought this dish to the attention of French chefs and it has since been widely adopted in France. In principle, there is no fixed recipe for this dish - any preparation of hot sauerkraut with meat and potatoes could qualify - but in practice there are certain traditions, favourite recipes, and stereotypical garnishes that are more easily called choucroute garnie than others.
Traditional recipes call for three types of sausage: Frankfurt sausages, Strasbourg sausages, and Montbéliard sausages. Fatty, inexpensive or salted cuts of pork also often form a part of choucroute garnie, including ham hocks, pork knuckles and shoulders, back bacon and slices of salt pork. Other recipes call for pieces of fish or goose meat, but this is far less typical. The sauerkraut itself is usually heated with a glass of Riesling or other dry white wines or stock, and goose or pork fat. In some recipes, it may also be cooked with chopped onion and sliced apples. Food writer Jeffrey Steingarten attempted to catalogue the composition of an authentic recipe in 1989. He writes that every traditional recipe includes black peppercorns, cloves, garlic, juniper berries, onions, and potatoes; most include bay leaves and wine.
Like cassoulet, pot au feu, and so many other examples of France's regional cuisine, choucroute's origin is in a traditional, inexpensive dish, but grand versions (such as Choucroute Royale, made with Champagne instead of Riesling), and grand ingredients (such as foie gras and wild game) are mentioned both in traditional sources (e.g. Ali-Bab) and in recipes from contemporary chefs and restaurants.
Choucroute garnie is available throughout France in canned or microwavable ready-to-eat form. A Hungarian version of choucroute garnie includes stuffed cabbage leaves in addition to the other ingredients. Shredded cabbage can also be added along with the sauerkraut in order to produce a somewhat less acidic version.)