Preheat the oven to 350°F (175°C). Grease an 8-inch round cake pan and line the bottom with parchment paper.

In a medium mixing bowl, whisk together eggs and sugar until light and frothy.

Add melted butter, vanilla extract, and rum (if using). Mix well.

In a separate bowl, combine flour, baking powder, and salt.

Gradually add the dry ingredients to the wet mixture, stirring until just combined.

Gently fold in the chopped apples until evenly distributed.

Pour the batter into the prepared cake pan and smooth the top.

Bake for 40-45 minutes, or until a toothpick inserted in the center comes out clean and the top is golden brown.

Let the cake cool in the pan for 10 minutes before transferring to a wire rack to cool completely.

Dust with powdered sugar before serving.