Allow butter to melt with garlic in dutch oven on stovetop over medium heat. Remove and discard outer leaves and stem of cabbage.
Cut in half and then slice into 1/2" slices. When butter is melted add into pot breaking up pieces. Stir to fold together and allow to simmer this way for 10 minutes.
Add chicken broth and sprinkle with salt and pepper if desired. Put lid on and reduce heat to low. Simmer this way for 20 minutes stirring twice in this time.
Lift lid and simmer uncovered for 5 minutes or until leaves as as tender as you'd like them to be. Turn heat off, fold in vinegar and taste. Add more salt and pepper to taste until just right. Serve.