1Remove the outer set of leaves of cabbage and discard. Cut cabbage quarters; remove and discard white stem. Chop remaining cabbage finely.
2Melt butter in a pot over medium heat. Cook and stir cabbage in melted butter until softened slightly, 2 to 3 minutes. Pour vinegar over cabbage and stir to coat. Add cranberry juice and sugar to the pot. Season cabbage mixture with salt.
3Reduce heat to low, place a cover on the pot, and cook, stirring occasionally, until the cabbage is completely tender, 60 to 75 minutes. Add more sugar towards the end if it is tart.