Continue to whisk until the butter mixture foams up and thickens to the consistency of a loose syrup (do not boil). Remove the pan from the heat. In a separate bowl, combine the vanilla and rum essence.
Spread the butter mixture over the cake, ensuring it gets into the holes. (Save approximately 1/4-1/2 cup of the mixture to brush around the edges of the cake.)
Allow for a 10-minute rest period or until the syrup is no longer sticky. (If you leave it sitting for too long, the cake will stick to the pan.)
Carefully remove the cake from the pan and set it aside for an hour to enable the cake to cool and absorb the syrup.
Reheat the remaining syrup and drizzle it over the cake.