Heat oven to 325 degrees F. Grease a 9x13 baking dish and set aside.
If you have two mixing bowls for your stand mixer, this is the time to break them out. Otherwise, just know there is a rinse coming up.
Seperate the eggs. Place the yolks in the bowl of your stand mixer and the whites in another bowl (Or additional mixing bowl if you have one).
Add the sugar to the egg yoks and beat on high until smooth, pale yellow, and thick, about 5 minutes. Transfer the egg yolks to another bowl, and clean out the mixing bowl well. Dry the bowl completely and add the egg whites. Whisk on high for 1 1/2 minutes, until moist peaks form.
Add about 1/3 of the egg yolk mixture to the whites and gently mix to combine. Add the remaining egg yolk mixture and fold until combined.
Whisk the flour in a bowl then sprinkle over the egg batter. Fold in, until no streaks remain, but being careful to not overbeat (and deflate) the batter.
Pour the batter into the prepared pan and bake for 20 to 25 minutes, until golden and pulling away from the sides of the pan.
Poke holes all over the top of the cake and allow to cool for 15 minutes.
Meanwhile, whisk the milks and 1 tablespoon rum together in a large bowl. Pour evenly over the cake.
Allow the cake to sit for 45 minutes longer. Wrap with plastic wrap tightly and let stand in fridge for at least 4 hours.
When ready to serve, toast the coconut in a preheated 325 degree oven for 3 to 5 minutes. whisk the heavy cream and powdered sugar.
Whisk the heavy cream, remaining tablespoon rum and powdered sugar in the bowl of your stand mixer until peaks form. Spread evenly over cake and sprinkle the coconut over top. Slice and serve.