Peel and core the apples and cut into thin pieces.
Melt the butter in a pan. Add sugar and stir slowly to form a uniform mass. Now add the apple pieces and stir slowly until they are a little bit coated with the sugar mixture on all sides - it takes about two minutes.
Mix the mulled wine with the rum aroma and cinnamon and then add to the pan. Let the whole thing simmer for 12-15 minutes. If there is not enough liquid in the pan, just add a little more mulled wine.
You can serve the mulled apples with vanilla pudding or vanilla sauce, for example.