1. Melt the butter in the microwave and let it cool. Preheat the oven to 350 degrees, then line the bottom of loaf pan with parchment paper.
2.In one bowl whisk together the flour, baking powder and salt. In another larger bowl add 1 cup plus 2 1/2 tablespoons sugar. Mix eggs in one at a time with a whisk. Mix in vanilla extract, heavy cream and 1 1/4 tablespoons rum.
3.Add half the flour mixture to the wet and stir until just blended, then mix in half of the cooled butter. Mix in the other half of the flour, then the butter just until it comes together with no lumps and no runny areas.
4.Pour the batter into the prepared loaf pan, then place the pans on a baking sheet. Bake for 50 minutes, then have a look to make sure there’s no wobble to the cake. Check for doneness by inserting a toothpick into the center; it should come out clean. If it is not done, bake for another 5 minutes and check again.
5.Cool for 5 minutes, then run a sharp knife around the edge to loosen the cake. Invert the pan, but then place the cake so their tops are facing up. While the cakes are cooling stir the water and 2 tablespoons sugar in a pot and bring to a boil. Take off the heat and stir in 2 tablespoons rum.
6.Poke holes through the cakes while it is still warm, with a skewer. Brush the cake with the rum syrup until all the syrup has been absorbed. When the cake has cooled, slice and enjoy!