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1
Preheat the oven to 325F.
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2
TO MAKE THE CAKE, bring the water to a boil and stir in the instant coffee, mixing until it dissolves.
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3
Put the cocoa in a heatproof bowl and pour the hot coffee into it, whisking until there are no lumps; set aside to cool.
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4
In a large bowl, sift together the flour, baking powder, baking soda, salt, and half of the sugar.
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5
In a separate bowl, combine the egg yolks, oil, and vanilla.
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6
Add the cooled cocoa mixture and gently stir with a whisk until smooth.
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7
Pour the egg mixture into the large bowl with the flour mixture, whisking until the batter is smooth.
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8
In a separate bowl, beat the egg whites with the salt and the cream of tartar until it starts to thicken.
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9
Add the remaining half of the sugar gradually and continue beating until stiff and glossy peaks form.
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10
Stir about one-third of the egg whites into the batter to lighten the mixture, then add the remaining egg whites in two parts, folding gently but making sure everything is well incorporated.
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11
Divide the batter into 2 ungreased 9-inch pans and bake until a toothpick inserted into the center comes out clean, 50 to 60 minutes.
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12
As soon as they come out of the oven, unmold the cakes onto a wire rack, and let them sit until cool.
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13
Remove the pans and prepare the tres leches mixture.
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14
TO MAKE THE TRES LECHES, bring the half-and-half to a boil in a small saucepan over medium heat.
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15
Put the chopped chocolate in a heatproof bowl and pour the hot half-and-half over.
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16
Allow to sit for a minute, then stir with a whisk until smooth.
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17
Whisk in the evaporated milk, salt, condensed milk, and rum, blending well.
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18
Put the cakes in a deep dish or back into their baking pans and pour the warm mixture over them.
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19
Be sure to pour any liquid that dripped down the sides on top of the cakes as well.
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20
Cover with plastic wrap and refrigerate for 2 to 4 hours, or freeze for 30 to 40 minutes, so they are easier to handle.
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21
TO MAKE THE FILLING, beat the heavy cream with an electric mixer or by hand until slightly thickened.
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22
Add the confectioners sugar and vanilla and continue beating until thickened and smooth.
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23
Refrigerate until the cakes have cooled.
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24
To assemble the cake, put one of the cakes on a piece of cardboard or a serving platter and spread about one-third of the filling evenly on top.
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25
Top with the second cake and cover the top and sides with the remaining filling.
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26
Holding the chocolate with a paper towel in one hand, use a peeler to shave the chocolate onto the cake.
