Cabbage burned (or browned) in butter (or any fat) is just downright delicious, especially in the winter! In what follows I use bacon but you can use butter or olive oil if you are vegetarian or vegan and it works well.
Try out 1/4 pound (or less) bacon, cut into tiny bits. Remove the crispy bacon to a bowl, but leave in the fat. Throw in a chopped onion and cook until soft. Add a half a cabbage, cut into small pieces. Stir it all up with lots of pepper and some salt and leave it there on medium heat until it starts to burn in the fat. Don't stir until it starts to really burn! Turn it once and let it start to burn again.
Now you have options: You can add cooked, drained pasta, a bit of cream, some grated parmesan cheese, and the bacon bits to make "cavolo pasta". You can add all of the above except the pasta to make a cabbage-as-pasta
non-pasta dish. You can just mix in the bacon and serve it as a side with anything (like latkes or sausages). Another improvisation that worked well was apples, sautéed with the cabbage.