Cut the duck skin and fat into small pieces and put in a saucepan with 1 cup water. Bring to a simmer and cook until the fat is melted and the skin is brown and crisp, 45 minutes to 1 hour. Scoop out the duck-skin cracklings, drain on paper towels and season with salt. Reserve the duck fat.
Preheat the oven to 425 degrees F. Heat 3 tablespoons duck fat (or olive oil) in a large skillet over medium-high heat. Brown the cabbage in batches, about 1 minute per side; transfer to a baking dish. Drizzle with 1 to 2 tablespoons duck fat (or olive oil), season with salt and toss. Roast until crisp on top, about 15 minutes, then turn the wedges and roast until the other side is crisp, about 8 more minutes. Sprinkle with the duck-skin cracklings and roast 2 more minutes. Drizzle with the vinegar.