Shred the cabbage finely. Melt the butter in a large heavy based saucepan (I have an old jam pan I use especially for rødkål as until it starts to cook down the cabbage takes up a lot of room!).
Add the cabbage and stir until the butter has been mixed through and the cabbage is all glossy.
Tip in the vinegar, apple, and a pinch of seasoning, along with a couple of tablespoons of water. Cook on a low heat for an hour, stirring periodically. If you find it is getting too dry add another spoonful of water; it should be moistly glossy but not sitting in a pool of liquid.
Add the redcurrant jelly and cook gently for another 45-60 mins, then season and start fiddling with the taste; I often add another couple of spoonfuls of jelly if I find it is not sweet enough. Cook until the cabbage is soft, rich and thick then leave overnight for the flavours to really develop. Warm gently to serve. Apparently it heats up very nicely in the microwave but I haven’t got one!
Notes
Not all vinegars are created equal! I find that apple cider vinegar can be much more acidic than white wine vinegar, so if yours is quite punchy add it spoonful by spoonful and taste as you go!