Preheat the oven to 350 degrees F. and grease a 10-inch springform pan with butter (alternately line it with parchment paper which will make the cake very easy to remove from the pan)

In a small bowl, whisk the flour, baking powder, and salt then set aside.

Peel, core, and thinly slice the apples.

In a large bowl, whisk the eggs for 1-2 minutes until they are foamy. Pour in the sugar, rum, and vanilla and whisk for another minute.

Whisk in half of the flour mixture until well-blended then blend in half of the melted butter. Repeat with the remaining flour and butter and blend until smooth.

Fold in the sliced apples, coating them completely with the batter then pour the mixture into the prepared pan.

Smooth the batter out then place in the pre-heated oven. Bake for 60 to 70 minutes until the cake is golden brown and a toothpick or knife inserted into the middle comes out without batter stuck to it.

Let the cake cool for 5 to 10 minutes then run a blunt knife around the edge of the pan to loosen any cake that may be stuck to the sides.

If the bottom of the pan is lined with parchment paper, the cake will slide out quite easily once the sides of the springform pan is removed. If the pan is not lined with parchment paper you will need to slide a long knife under the bottom of the cake to loosen it from the pan then invert it onto a plate that is lined with parchment paper then invert it again onto a serving platter (this will be accomplished easier if you allow the cake to cool completely)