Preheat your oven to 350°F (175°C) and grease an 8-inch springform pan with butter.
Peel, core, and chop the apples into 1/2-inch chunks. Set aside.
In a small bowl, whisk together the flour, baking powder, and salt.
In a larger bowl, use an electric mixer to beat the eggs and sugar until the mixture is pale. Add the rum and vanilla, whisking to combine.
Gradually incorporate the flour mixture and melted butter into the batter, alternating between the two in halves. Stir gently after each addition.
Fold the chopped apples into the batter until evenly coated. It may seem like there are too many apples, but that’s exactly right!
Spread the batter into the prepared pan, smoothing the top with a spatula. Sprinkle 2 tablespoons of sugar over the surface.
Bake for around 45 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for 15 minutes before carefully removing. Serve and enjoy!