1. Preheat the oven to 350 degrees F and center a rack in the oven. Butter an 8 inch springform pan. Line a baking sheet with a silicone baking mat or parchment paper and put the springform pan on it. Set aside.

2. Whisk the flour, baking powder, and salt together in a small bowl.

3. Peel the apples, cut them in half, and remove the cores. Cut the apples into 1 to 2 inch chunks.

4. In a medium bowl, beat the eggs with a whisk until foamy. Pour in the sugar and whisk until smooth. Whisk in the rum and vanilla. Whisk in half of the flour mixture, when it's incorporated, add half of the melted butter, followed by the remaining flour mixture and butter. Mix in between additions so you have a smooth, thick batter.

5. Fold in the apples with a rubber spatula. Pour batter into prepared pan. Spread with spatula so the batter is somewhat even.

6. Slide the pan in the oven and bake 50-60 minutes, or until the top of the cake is golden brown and a knife inserted in the center comes out clean. Transfer to a cooling rack and cool for five minutes.

7. Run a knife around the edges of the cake and remove from the pan. Cool cake until slightly warm or at room temperature. If you want to remove the cake from the pan, wait until the cake is completely cooled. Slide a long spatula between the cake and pan, cover the top of the cake with a piece of parchment or wax paper, and invert it onto a rack. Carefully remove the bottom of the pan and turn the cake over onto a serving platter.

*Note-you can serve the cake with vanilla ice cream or whipped cream. Dorie suggests not covering the cake because it is so moist. Just press a piece of plastic wrap against the cut surfaces of the cake.