For the cake:
In the bowl of a mixer, beat eggs until light yellow in color.
In a separate bowl, sift together sugar, flour, and baking powder.
While mixing on low, add the dry ingredients to the eggs until combined.
Add melted butter and milk, mix to combine.
Spray a metal 12x10 inch pan and line with parchment paper.
Preheat oven to 350 degrees. Set up a steam bath in your oven by placing a deep pan on the bottom rack. Once you add the cake to the oven you'll want to fill the deep pan with hot water and close the oven quickly to trap the steam.
Pour batter into lined pan and seal tightly with plastic wrap and then foil on top.
Steam for 15 minutes and then check with a cake tester or toothpick to make sure it's cooked through.
Cut the cake into 12 equal-sized pieces.
Make the milk soak:
Combine all three kinds of milk in a bowl and whisk together.
Pour milk mixture over the cut cake pieces in the pan and let it soak in the fridge.
For the sauce:
Dice the pineapple into 1/4 inch pieces, setting half of it aside for later.
Add rum, half of the pineapple, and vanilla bean pod to a small pot. Allow to come to a simmer for 10-15 minutes until juices are reduced, adding water by the tablespoon as needed.
Once reduced to a thick syrup, remove mixture from heat. Add juice of the lemon and allow to cool.
While it cools, finely chop basil and mint. Add reserved pineapple and chopped herbs to cool sauce.
Serve cake with pineapple rum sauce over the top.