Preheat your oven to 350°F (175°C). Grease a 9-inch bundt pan or a round cake pan with butter, then lightly flour the pan or use non-stick cooking spray to prevent the cake from sticking.

In a medium bowl, sift together the flour and baking powder. Set aside.

In a large mixing bowl, beat the butter and granulated sugar together until light and fluffy (about 3-4 minutes). You can use a hand mixer or stand mixer for this step.

Add the eggs and egg yolk, one at a time, beating well after each addition. Then add the seeds scraped from the vanilla beans or vanilla extract and mix until fully incorporated.

Gradually add the sifted flour mixture, alternating with the milk and rum, beginning and ending with the flour mixture. Mix until just combined, being careful not to overmix.

Pour the batter into the prepared bundt pan and smooth the top with a spatula. Bake for 50-60 minutes, or until a toothpick inserted into the center of the cake comes out clean. Once baked, allow the cake to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.

While the cake is cooling, make the glaze. In a small saucepan, melt the butter over medium heat. Add the sugar, water, and rum, stirring occasionally until the sugar dissolves completely and the mixture begins to boil. Let it simmer for about 3-5 minutes until it thickens slightly.

Once the cake has cooled to room temperature, use a skewer or fork to poke several holes in the cake. Pour the warm rum glaze evenly over the cake, allowing it to soak in. Let the cake sit for at least 30 minutes to absorb the glaze before serving.