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In a large skillet, heat butter and oil over medium heat; add cabbage, garlic and brown sugar to pan.
Sauté until the cabbage is limp, about 5 minutes or so.
Reduce heat to medium-low and stir in vinegar.
Cook, stirring very often, for approximately 20 minutes; taste and if cabbage is too crunchy for you, continue to cook for a few more minutes.
Add salt and pepper to taste and serve.