Prepare the sausage for roasting: if necessary, prick it a few times with a toothpick to prevent the fat from bursting out during cooking.
In a skillet or oven, roast the sausage over medium heat for 15-20 minutes, turning occasionally, until golden brown on all sides. For oven roasting, preheat the oven to 350°F (180°C).
While the sausage is roasting, prepare the cabbage: remove the outer leaves, then halve it and shred or slice it into thin strips.
Peel and finely chop the onion. Heat the oil in a large skillet, then sauté the onion until translucent, about 5 minutes.
Add the cabbage, then season with salt and pepper, and sprinkle with sugar. Stir and sauté for 10 minutes, until the cabbage is slightly softened.
Pour in the apple cider vinegar, then continue to braise for another 5-10 minutes, until the cabbage is fully tender but still slightly crisp.
When serving, place the roasted sausage next to the braised cabbage, and offer freshly grated horseradish on the side, which adds a characteristic flavor to the dish.
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