Step 1: Preheat your oven to 350°F. Grease and flour a 10-inch bundt pan and set it aside.

Step 2: In a medium bowl, whisk together the flour, baking powder, and salt. Set the dry ingredients aside.

Step 3: In a large bowl, beat the butter and sugar together until light and fluffy. Add the eggs one at a time, beating well after each addition.

Step 4: Add the dry ingredients to the butter mixture in three parts, alternating with the milk. Mix until just combined.

Step 5: Stir in the rum and vanilla extract.

Step 6: Pour the batter into the prepared pan and smooth the top with a spatula.

Step 7: Bake for 50-60 minutes, or until a toothpick inserted into the center of the cake comes out clean.

Step 8: While the cake is baking, make the caramel sauce. In a small saucepan, melt the butter over medium heat. Add the sugar and stir until it dissolves. Gradually add the rum, stirring constantly. Simmer for 3-4 minutes, or until the sauce thickens slightly.

Step 9: When the cake is done, remove it from the oven and let it cool in the pan for 5-10 minutes. Then, invert the cake onto a wire rack and allow it to cool completely.

Step 10: Once the cake has cooled, brush the caramel sauce over the top and sides of the cake, making sure to cover every inch.