Clean leeks and slice into 1/2 inch rounds. Divide cabbage into two quarters and roughly chop them into chunks, avoiding the core. Separate the cabbage pieces slightly.
Heat a large pot over medium heat. Add olive oil and butter and heat until butter is bubbling.
Add leeks and sauté for 2 minutes. Add the cabbage and immediately stir thoroughly to coat the cabbage with butter. Season with salt and pepper.
Partially cover and cook on medium heat for about 7 minutes, stirring often, until cabbage has wilted significantly. During this time, quarter and core the apple and roughly dice.
Add the apple and vinegar to the cabbage. Continue cooking on medium heat for another 3 minutes, stirring often. Taste for seasoning and adjust if necessary.
adapted from simplebites.net