A take on braised cabbage

I am in the midst of exams here at law school, so for the past two weeks, I haven't made anything very inventive. At the farmer's market one day, I bought a head of cabbage, because I felt like I needed a vegetable, and I'm Polish, German and Irish - all good cabbage-loving people. I looked at some recipes on the internet for braised cabbage, and decided to try to do a variation of them for the slow cooker, so I could leave it while I went to school to study. I must say, it turned out pretty well. I've been eating it with pearl barley. I also think it would be good alongside mashed potatoes or boiled fingerlings, and would be a great accompaniment to pork or sausage.

(all measurements are approximate, since I kind of made it up)

1 head cabbage (I used green, but I think red would be even better), cored and chopped
Carrot (probably the equivalent of 3), cut in coins
1 onion, sliced (I used some white and some red, since that's what I had)
1 apple, peeled, cored and diced
3 TBSP apple cider vinegar
1/2-1 c of water (you could probably also use stock if you want)
1 TBSP butter, cut into pats
A pour or two of olive oil
Salt and pepper to taste

Place the prepared vegetables in the crock pot and mix up as best you can. (I had a really big head of cabbage, so it was hard to mix much.) Pour in the vinegar and water, and place the pats of butter on top. Pour a bit of olive oil over it, and sprinkle with salt and pepper. Set the cooker on low and go about your business.

Results: Mine was super tender and browned. Also, don't be alarmed if the pot is really full, because it will all cook down. I probably left it a bit too long - 10 hours or so - because I'm busy, but it still tasted good. I bet 5-6 hours would be sufficient, but since you're going for soft anyway, it doesn't really matter how long you leave it. Warning: this will make your house smell like cabbage!