Whisk together the cocoa, instant coffee, and warm water until fully dissolved and smooth.
Separate the egg yolks from the egg whites. Set egg whites aside in a small bowl. Whisk egg yolks and sugar together until smooth. Add vegetable oil to the mix and whisk.
Slowly, stir in the cocoa and coffee mixture.
In a separate bowl, whisk together the flour, baking powder, and baking soda. In thirds, mix the flour into the wet ingredients until well-combined.
Add salt to the bowl of egg whites. Beat until the whites turn into a thick, sturdy foam. (Note: The foam should be so thick that if you were to flip the bowl upside-down they wouldn't fall out.)
Slowly and in small portions, fold the foam egg whites into the batter until just combined. Be careful not to over mix.
Pour the batter into a cake pan and bake in a preheated 300°F oven for about 50 minutes. Check the doneness of the sponge cake by inserting a toothpick into the center. If it comes out clean, the cake is ready.
Remove the cake from the oven. Let the cake cool to room temperature. Carefully slice it into four layers. In a small bowl, whisk together the sweetened condensed milk and heavy whipping cream to make the cake soak. Transfer the mixture into a squirt bottle or gently spoon it over the cake layers.