Preheat oven to 350°F. Place 3 mini cake pans on a baking sheets. Set aside.

Whisk together the flour, baking powder and salt. Set aside.

Peel the apples, cut them in half to remove the core and slice into 1 to 2 inch chunks.

In a medium mixing bowl whisk the eggs until foamy. Add the sugar and whisk until blended. Add the rum and vanilla and whisk to combine. Add half the flour and once blended, add half the melted butter. Repeat by adding the remaining flour gently whisking until combined, then add the remaining melted butter. Do not beat but gently fold in the apples with a rubber spatula. Divide the batter between the three baking pans. Using a table knife, poke the batter to help distribute the apples evenly.

Bake for 60 minutes or until the top is lightly browned and a knife inserted in the center comes out clean. Remove the cakes to a cooling rack and gently run a blunt knife around the outside edge to loosen the sides. Cool completely in the paper baking pans.

Store at room temperature, May be served slightly warm. Apple cake may also be baked in a 8" greased spring form pan.

Add the apple cider to a medium saucepan. Heat on high until it comes to a boil. Reduce the heat to medium or medium-low to maintain a gentle boil. Cook for 20 minutes or until the cider is reduced in half. Remove from the heat and add the cinnamon, vanilla and butter. Whisk in the powdered sugar until smooth. When ready to serve, drizzle over fresh apple cakes or ice cream.