Preheat the oven the 350F.
Cut out a parchment paper round and line the bottom of a springform pan.
Mix the flour and baking powder in a bowl. If you are using unsalted butter, add a pinch of salt to the bowl (about 1/8 tsp).
Peel and chopped the apples.
Use a hand mixer to cream the sugar and butter but if you don’t have one, use a stand mixer fitted with a paddle attachment.
Add eggs one at a time until completely incorporated.
Add the vanilla and rum.
Add the flour one spoon at a time until completely mixed.
Fold in the chopped apples using a spatula.
Pour onto the center of the prepared springform pan and push the mixture out towards the edges.
Bake at 350F for 40 minutes or until a inserted toothpick comes out clean.
Remove from oven and place on a wire rack to cool for a few minutes.
Run a blunt knife along the edge to release the cake from the walls of the springform pan and open the clamp.
Allow the cake to cool further.
Cool completely or you can also serve it warm with a scoop of ice cream.