I love cooked red cabbage, done in my crockpot. It is sweeter than green cabbage and the touch of vinegar would give the pickled taste.
Here's a very simple recipe that is worth making:
1 head red cabbage
1 onion -- finely chopped
1 dash salt -- to taste
3 tablespoons butter -- add later
2 tablespoons vinegar -- add later
Shred cabbage finely and cook in boiling salted water with the onion until almost tender. Drain.
Add butter and vinegar; stir well.
Support bacteria. It's the only culture some people have.