Sauté the cabbage: Melt the butter in a large pot over medium heat. Add the thinly sliced red cabbage and toss to coat with the butter. Sauté until slightly wilted, about 5 minutes.
Add the sugar and vinegar, simmer: Sprinkle sugar over the cabbage and toss to coat evenly. Add the balsamic vinegar to the pot. Bring to a simmer, then reduce the heat to medium low. Cover and simmer until the cabbage is completely tender but not mushy. Stir often, about 30 to 45 minutes total.
Season: Season to taste with salt and pepper. Did you enjoy this recipe? Let us know with a rating and review!