Preheat oven to 180°C (350°F). Grease and flour an 8-inch square or 9-inch round pan.

Sift together flour, baking powder, and cinnamon in a large bowl.

In a separate bowl, beat eggs, oil, vanilla, cream, buttermilk, sugar, and rum until fluffy.

Add the flour mixture to the wet ingredients and mix until just combined.

Gently fold in most of the sliced apples, reserving some for the top.

Pour the batter into the prepared pan and spread evenly.

Arrange the remaining apple slices on top of the batter, pressing them lightly into the cake.

Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.

Let the cake cool completely in the pan before slicing and serving.