To make Danish sweet braised red cabbage, the first step is to chop the cabbage. Remove the outer leaves, cut it into quarters, and cut out the core. Lay it on its cut side and slice it into about 1/4–1/2-inch strips (1/2–1 cm).
Melt the butter over medium heat in a large pot. Add the cabbage, vinegar, red currant jelly or jam, water, and salt.
Cook for about one hour over low-medium heat, stirring often so it does not stick. Cook it covered for the first 15 minutes, then uncovered. It is important that by the end, most of the liquid has cooked away and a glossy, thick sauce remains, completely coating the cabbage. To achieve this, you may need to cook it over high heat for the last few minutes, stirring regularly.