Preheat the oven to 350 degrees F. Grease a regular bundt pant, or mini bundt pan with butter and sprinkle with flour. Shake out the excess over the sink.
Make the baba. In a saucepan, combine the milk, butter, and vanilla bean and seeds over medium heat until hot but not boiling.
Meanwhile, sift together the flour, baking powder, and salt.
In a large bowl, whisk together the egg yolks and granulated sugar until smooth. Whisk in the hot milk mixture and then the flour mixture.
Using an electric mixer, whip the egg whites until they hold stiff peaks. Gently fold them into the batter.
Pour the batter into the prepared pan and bake until golden brown and a toothpick inserted in the baba comes out clean- about 25-30 minutes. Let cool for 10 minutes and then unmold onto a rimmed serving platter.
Prepare the rum syrup. In a small saucepan, bring the granulated sugar and 1/2 cup of water to a boil. Add the rum, reduce the heat, and simmer just until the sugar dissolves.
Whip the cream and powdered sugar until the cream holds stiff peaks.
Slowly pour the rum syrup all over the cake and wait until it is fully absorbed. Serve with whipped cream and a drizzle of any pool rum syrup.
Notes
Adapted from French Country Cooking by Mimi Thorisson