Melt butter in a nonstick skillet. Add apples and sprinkle with sugar. Saute, stirring constantly with a wooden spoon until apples begin to get tender, about 2 to 3 minutes.
Add currants and saute for another couple of minutes to heat them through and continue to cook the apples. Remove the skillet from the heat, stir in the rum and swirl the apples around until it is absorbed. If you wish, top with chopped nuts, whipped cream or vanilla ice cream.