1. Preheat the oven to 350ºF (180ºC) and adjust the oven rack to the center of the oven.
2. Heavily butter an 8- or 9-inch (20-23cm) springform pan and place it on a baking sheet.
3. In a small bowl, whisk together the flour, baking powder, and salt.
4. Peel and core the apples, then dice them into 1-inch (3cm) pieces.
5. In a large bowl, beat the eggs until foamy then whisk in the sugar, then rum and vanilla. Whisk in half of the flour mixture, then gently stir in half of the melted butter
6. Stir in the remaining flour mixture, then the rest of the butter.
7. Fold in the apple cubes until they’re well-coated with the batter and scrape them into the prepared cake pan and smooth the top a little with a spatula.
8. Bake the cake for 50 minute to 1 hour, or until a knife inserted into the center comes out clean. Let the cake cool for 5 minutes, then run a knife around the edge to loosen the cake from the pan and carefully remove the sides of the cake pan, making sure no apples are stuck to it.