Preheat the oven 350 F. Butter an 8 inch springform pan and place on a baking sheet.

Mix the flour and baking powder together.

In a separate bowl, whisk the eggs until foamy. Add the sugar and whisk. Whisk in the rum and vanilla. Then whisk in half of the flour and then half of the butter. Repeat with the remaining flour and butter. Fold in the apples with a spatula and coat the fruit. Spread the batter in the pan.

Bake the cake for 50-60 minutes or until the top of the cake is golden brown and a toothpick inserted in the center comes out clean. Let cool for 5 minutes. Open the springform pan and let cool on the pan bottom. When slightly warm, invert the cake onto a plate and remove the pan bottom. Invert the cake again if you would like.

Serve with whipped cream or vanilla ice cream. May keep at room temperature with only the cut sides covered with plastic wrap; do not cover the cake.