Preheat oven to 325 with the rack in the middle position. Butter a 9×13 baking dish. Set aside.

Separate eggs. Place whites in mixer and beat on high speed until medium peaks form, about 1 1/2 minutes. Transfer to another bowl.

Place egg yolks in mixing bowl and add sugar. Beat on high, until pale yellow, about 5 minutes. Stir in vanilla.

Using a rubber spatula, stir about 1/3 of the whites into the yolk mixture to lighten it. Then gently fold in the remaining whites. Sprinkle the flour over the egg mixture and gently fold it in, until there are no white flour streaks remaining.

Pour the batter into the pan and bake until the cake is puffed and golden around the edges about 20-25 minutes.

Meanwhile! Place the three milks and the rum in a large bowl and whisk until combined.

Remove cake from oven and place on a cooling rack. Using a toothpick or skewer, poke holes all over the cake and allow to cool for 15 minutes. Poke holes at least every 1/2 inch and poke all the way to the bottom. Pout the milk mixture evenly over the cake and continue cooling about 45 more minutes.

Refrigerate at least four hours or overnight.

To make frosting:
Toast coconut for topping. Set aside. Beat cream until soft peaks form. Then add rum and powdered sugar. Continue beating until stiff peaks form. Refrigerate until ready to use. When ready to serve cake, frost with whipped cream and sprinkle with toasted coconut. Or just dollop the way we did!