This is another of my recipes for Oktoberfest, and our family usually has it for either Thanksgiving or Christmas also. It is a traditional German dish that my mother made all the time for our family. It is so delightfully simple and tasty.
Remove outer leaves of cabbage if wilted or damaged. Cut head in half, remove hard core and shred/chop coarsely as for a rough coleslaw.
Heat oil in either a 12 inch skillet or a large saucepan over medium high heat. Add chopped cabbage and stir well to cover with oil. Saute cabbage until it begins to get limp, stirring occasionally. Add optional chopped apple if using. Add 1/4 cup of water to pan and cover to steam cabbage til almost tender.
Remove cover and let any moisture evaporate. Reduce heat to medium. Add and melt the butter. Add flour and stir until incorporated. Cook for a minute or two to cook out the raw flour taste.
Measure vinegar into cup with remaining 1/4 cup water, add to cabbage along with sugar. Stir well.
Stir until flour/butter/water/vinegar/sugar mixture has thickened. Add salt and pepper to taste. This dish takes a fair amount of salt to bring out the sweet and sour flavor. I use about 1/2 tsp or more, but you will need to adjust to your taste.
Keep warm and serve with your favorite meat dish. This is particularly good with roast chicken or turkey, beef roast or pork chops/cutlets.