1. Preheat the oven to 350°F (175°C) and line an 8-inch springform pan with parchment paper, then butter the sides.

2. Peel, core, and thinly slice the apples. Toss with a squeeze of lemon juice to prevent browning.

3. In a large bowl, cream together the melted butter and granulated sugar until smooth and pale.

4. Add the eggs one at a time, whisking after each addition, then stir in the vanilla extract and rum or apple juice if using.

5. In a separate bowl, sift together the flour, baking powder, and salt.

6. Gradually fold the dry ingredients into the wet mixture until just combined, taking care not to overmix.

7. Gently fold the apple slices into the batter, ensuring they are evenly coated.

8. Pour the batter into the prepared pan, smooth the top, and arrange a few decorative apple slices on the surface.

9. Bake for 40–50 minutes, or until the top is golden and a toothpick inserted into the center comes out clean.

10. Allow the cake to cool in the pan for 10 minutes, then release the springform and transfer to a cooling rack. Dust with powdered sugar before serving.