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Generously season chicken with sea salt and pepper. Heat 1 tablespoon in a large skillet over medium. Place chicken thighs, skin side down, in skillet and sear until skin is browned and crisp, 10–12 minutes. Flip the chicken and continue until cooked through, 8–10 minutes longer. Remove thighs from pan and set aside to rest.
Pour off some of the fat from skillet and increase heat to medium-high. Add the onion, caraway seeds, and a pinch of salt to the pan. Sauté until the onion is completely softened and just starting to caramelize. Add some of the cabbage, and toss to coat. Continue to cook until the cabbage wilts.
Add the stock and wine. Simmer uncovered for 10 minutes, and then add the remaining cabbage. Continue to simmer until the second addition of cabbage is softened, and almost all of the liquid is cooked off, about 5 minutes, stirring occasionally.
Whisk together the cream and mustard with a fork, and stir into the cabbage. This is the step that makes this braised cabbage dish so special.
Serve Chicken thighs with braised cabbage.