To Make the Batter
In a large bowl, mix egg yolks, flour, sugar, and salt until combined (will be lumpy). Mix in beer until batter is smooth. Set aside and ideally let rest for 1 hour.
In a medium bowl, beat egg whites until stiff. Gently fold into beer mixture.
For the Apples
Sprinkle 1/2 inch thick apple slices with rum.
Heat the oil until very hot. Dip the apple slices into the batter and fry in the hot oil until golden brown, about 4 minutes per side (flip apple slices to make sure both sides brown). Remove with a slotted spoon and transfer to a paper towel lined plate. Sprinkle with confectioner's sugar or favorite syrup.