Braised Red Cabbage with Chestnuts

Heat oil in a large pot or Dutch oven over medium heat. Add onions and cook, stirring often, until light golden, 6 to 8 minutes. Add cabbage and cook, stirring occasionally, until the cabbage wilts, about 5 minutes. Stir in broth, sugar and caraway seeds; bring to a simmer. Reduce heat to low, cover and cook until the cabbage is very tender, 15 to 20 minutes. Stir in chestnuts, vinegar, salt and pepper. Increase heat to medium and cook, uncovered, until most of the liquid has evaporated and the chestnuts are hot, 5 to 8 minutes.