Bring hearty elements together for a great winter dish. Slideshow: More Cabbage Recipes
In a large heavy pot, heat the butter over medium high heat until hot, then brown the sausages, turning once, about 5 minutes. Transfer the sausages to a platter.
Stir in the onion, apple, garlic and 1/2 teaspoon each salt and pepper, then cook, stirring occasionally, until golden, about 6 minutes.
Place the sausage back in the pot along with the cabbage, beer, Worcestershire, mustard, and caraway and bring to a boil. Reduce heat to a simmer, then cook, covered, until cabbage is tender, about 20 minutes. Uncover pot and simmer until liquid is almost evaporated, about 5 minutes, then season with salt and pepper to taste, sprinkle with the dill and serve.