Preheat your oven to 325 degrees F.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and the sugar together on medium speed for two minutes.
Gradually add the egg whites, making sure to scrape down the sides and the bottom of the bowl between additions. Mix on medium-high for 2 minutes after all the eggs are added.
Add the coconut emulsion and vanilla extract.
In a medium size mixing bowl, whisk the cake flour, baking powder, lime zest and salt.
Turn the mixer on low speed and alternately add the flour mixture and the coconut cream, starting and ending with the flour mixture. Mix until combined.
Evenly distribute the batter over the graham cracker layers (if making with a crust), or pour into prepared pans with no crust, in the three pans and level with an offset spatula.
Bake for about 23-25 minutes, or until the tops are slightly golden brown and the edges of the cake start to pull away from the sides of the pan. Don't turn off your oven.
Let cool in pans for 10 minutes and then invert onto cooling racks to cool completely.