Slice the cabbage wedges finely by hand. Transfer to a large saucepan or Dutch oven. Quarter, core and peel the pear.
Grate the pear on the coarse side of a four-sided grater. Add to the saucepan along with the butter, 2 Tbsp balsamic vinegar, brown sugar. Season to taste with salt and pepper.
Cover and cook over medium-low heat, stirring often until cabbage is tender, about 30 minutes. Taste and adjust seasoning, adding another splash of balsamic vinegar if necessary.
Serves 4