Preheat your oven to 400°F. Lightly grease just the bottom of a 9x13x3 cake pan.
Sift the cake flour and cocoa powder together two times. Set the dry ingredients aside.
In a large mixing bowl combine the yolks, vanilla bean paste, and 4 ounces (114g) of the sugar. Whip this mixture on high for 5-7 minutes, or until they are a very pale yellow and the beaters leave ribbons in the mixture. Gently fold the warm water into the egg yolks. Set this aside while you whip the egg whites.
Whip the egg whites until they begin to foam. Increase the mixer's speed to medium-high and shake in the remaining sugar and the salt. Increase the speed once more to high and whip for another 6-8 minutes.Beat the egg whites until they hold a stiff peak when the beaters are lifted from the bowl.
Mix and Bake the Cake Batter
Immediately sift half of the dry ingredients into the bowl of yolks. Use a large rubber spatula to gently fold the flour mixture into the eggs.Once the flour is absorbed add half of the egg whites to the flour-yolk bowl. Again, fold gently, until the mixture is well-mixed.Fold in the remaining flour, followed by the rest of the whites- folding each in just until everything is blended.
Scrape the batter into the prepared pan and bake for 20 minutes- or until the cake offers a bit of resistance when you press its surface.
Remove the baked cake from the oven and allow it to cool in the pan. Use a sharp knife to separate the cake from the sides of the pan.Once the cake is cool, use a toothpick to poke small holes in it.
Combine the Tres Leches
In a pitcher, whisk the chocolate, evaporated, and condensed milk until the condensed milk is fully incorporated.
Slowly pour the tres leches over the surface of the cake. Pour in stages to allow the cake time to absorb the milk. Cover the cake with plastic wrap and- carefully- put it in the fridge. Allow the cake to soak for 4-12 hours (or overnight).
Decorate and Garnish the Tres Leches
An hour prior to serving the tres leches, whip the heavy cream and powdered sugar to stiff peaks.Spread a generous heaping of the whipped cream onto the cake.
Drizzle the cajeta over the cake. Return the tres leches to the fridge and allow the whipped cream to settle on the cake for at least an hour.
Keep the cake refrigerated. Enjoy your tres leches within 48 hours.
If you have a stand mixer and are good at multi-tasking, you can whip the egg whites at the same time as the yolks.