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1
Heat the oven to 325 degrees F and arrange a rack in the middle.
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2
Coat the sides and bottoms of 2 (9-inch) cake pans with butter.
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3
Cut 2 rounds of parchment paper and place in the bottoms of the pans.
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4
Butter the tops of the parchment and dust the pans with flour, tapping out the excess; set aside.
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5
Place the water in a small saucepan and bring to a boil over high heat.
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6
Remove from the heat, add the instant coffee, and stir until dissolved.
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7
Place the cocoa powder in a medium heatproof bowl and whisk in the hot coffee until there are no lumps.
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8
Let cool slightly, about 15 to 20 minutes.
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9
Sift the measured flour, baking powder, baking soda, 1/2 teaspoon of the salt, and 1/2 cup plus 2 tablespoons of the sugar into a large bowl; set aside.
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10
Place the egg yolks, oil, and vanilla in a separate large bowl and whisk until combined.
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11
Pour the cooled cocoa mixture into the egg mixture and gently whisk until smooth.
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12
Pour the egg mixture into the flour mixture and whisk until the batter is smooth; set aside.
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13
Place the egg whites, the remaining pinch of salt, and the cream of tartar in the bowl of a stand mixer and beat on medium-high speed until the egg whites begin to turn white and foamy, about 1 to 2 minutes.
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14
Slowly add the remaining 1/2 cup plus 2 tablespoons sugar, about 1 minute.
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15
Continue beating until stiff and glossy peaks form, about 2 minutes more.
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16
Using a rubber spatula, stir about one-third of the egg whites into the batter to lighten the mixture.
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17
In two additions, gently fold in the remaining egg whites, making sure no white streaks remain but being careful not to deflate the whites.
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18
Equally divide the batter between the prepared pans.
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19
Bake side by side, rotating halfway through the baking time, until a toothpick inserted into the center comes out clean, about 40 to 45 minutes.
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20
Cool the pans on a rack for 10 minutes, then unmold the cakes onto the rack to cool completely.
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21
Wash the cake pans.
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22
Using a serrated knife, trim a very thin layer from each cake top, just enough to even out the surface and expose the inside of the cake.
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23
Return the cakes to the cleaned cake pans; set aside.
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24
Place the chocolate in a large, heatproof bowl.
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25
Place the half-and-half in a small saucepan over medium heat and bring it just to a boil.
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26
Pour the half-and-half over the chocolate and let it sit until the chocolate has softened, about 1 minute, then whisk until smooth.
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27
Whisk in the condensed milk, evaporated milk, rum, and salt until smooth and combined.
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28
Divide the tres leches mixture into 2 equal portions.
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29
Starting with 1 cake and 1 portion, pour as much of the tres leches mixture over the cake as possible.
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30
Repeat with the second cake and tres leches portion.
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31
Set the cakes aside until they begin to absorb the mixture, about 20 minutes.
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32
Continue to add more of the mixture until all of it has been added, about 30 to 40 minutes more.
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33
Cover the cakes with plastic wrap and refrigerate 4 hours, or freeze 1 1/2 to 2 hours, until the cakes are easier to handle.
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34
(They may not completely absorb all of the mixture.)
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35
Turn the cakes out of the pans by inverting each onto a plate over the sink, as some unabsorbed mixture may spill out.
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36
Place the cream in the bowl of a stand mixer fitted with a whisk attachment and whip until slightly thickened.
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37
Add the powdered sugar and vanilla and continue beating until thickened and smooth.
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38
To assemble the cake, place 1 of the cakes on a serving platter.
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39
Using an offset spatula or long, thin knife, spread about one-third of the filling evenly on top.
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40
Place the second cake on top and evenly spread the remaining filling over the top and sides of the entire cake.
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41
Refrigerate for at least 15 minutes to let the whipped cream set.
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42
Just before serving, garnish the cake: Hold the piece of chocolate with a paper towel in one hand, and use a vegetable peeler to shave the chocolate all over the top of the cake.
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43
Serve immediately.
