Put the cabbage, leeks, celery, and cherries in a large pot.
Cook over medium heat, stirring frequently, for 10 minutes.
Add the vinegar, decrease the heat to medium-low, cover, and cook, stirring occasionally, for 30 minutes.
Uncover and cook, stirring occasionally, for 10 minutes longer, or until the cabbage is dry.
Add the thyme stir until evenly distributed.
Serve hot.