Preheat oven to 400F
Pan-fry cabbage in half the butter on medium heat until soft. Do not let it brown, approx 10 minutes.
Add spices and vinegar, continue to fry for 3 minutes.
Set aside in a large bowl.
Saute the ground beef with the remaining butter at medium-high heat, until most of the liquid has evaporated.
Reduce to medium-low, toss in cabbage, cook for 3 minutes.
Add salt&pepper to taste.
Stir in 2/3 of the cheese and cook for another minute.
Place in casserole dish, cover with remaining cheese.
Bake until top is golden brown, approx 15-20 minutes.