Heat butter in medium skillet, over medium heat. Add cabbage, saute for 1 minute. Add caraway seeds and apple cider, and bring to a boil. Reduce to a simmer, and cook, stirring occasionally for 6 to 7 minutes. Add 1 tablespoon cider vinegar, and cook for 1 minute more. Remove from heat, and season with salt and pepper to taste. Serve immediately.