Preheat oven to 350°F (175°C).

In a large mixing bowl, cream together the butter and sugar until light and fluffy.

Beat in the eggs, one at a time, until well combined.

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

Gradually add the flour mixture to the butter mixture, alternating with the milk, and mix until just combined.

Stir in the rum and vanilla extract.

Pour the batter into a greased 9-inch cake pan.

Bake for 35-40 minutes, or until a toothpick inserted into the center of the cake comes out clean.

Allow the cake to cool for 10 minutes, then remove from the pan and transfer to a wire rack.

While the cake is still warm, prick the top all over with a fork and pour the remaining rum over it.

Allow the cake to cool completely before serving.