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To make the chocolate cake: Preheat the oven to 350F.
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Spray an 11 x 17-inch rimmed baking sheet with nonstick cooking spray, line with parchment paper, and spray the paper.
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Set aside.
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Sift the cocoa, flour, and cornstarch together and set aside.
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Put the egg whites in the bowl of an electric mixer fitted with the whisk attachment and whisk at medium-high speed until frothy.
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With the machine running, slowly add 1/3 cup of the sugar and continue whisking until medium-soft peaks form.
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(When you lift the whisk from the mixture, a peak will form and the top of the peak will fall back down.)
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Transfer the whipped whites to a large bowl.
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Put the yolks in the electric mixer bowl and whisk on medium speed until the yolks break.
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With the machine running, add the salt and the remaining 1/3 cup sugar in a slow, steady stream.
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Continue whisking until the mixture is pale yellow, thick, and doubled in volume, about 12 minutes.
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Whisk half the whites into the yolk mixture until fully incorporated, then gently fold in the dry ingredients until no traces of flour or cocoa remain.
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Add the remaining whites to the mixture and fold gently until only a few white streaks remain.
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Whisk the oil and buttermilk together until smooth and homogenous, then fold into the batter until completely incorporated.
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Spread the batter evenly in the baking sheet.
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Bake for 5 minutes, then rotate the pan and bake until a tester comes out clean, about 5 more minutes.
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Cool completely in the pan on a rack.
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Meanwhile, make the mousse: Put the milk, sugar, and salt in a small saucepan, stir well, and set over medium heat.
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Warm just until bubbles form around the edges, then whisk in the Horlicks until completely dissolved.
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Remove from the heat.
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Put the yolks in a large mixing bowl and whisk until the yolks break.
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Add the warmed Horlicks mixture in a steady stream while whisking constantly.
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Return the mixture to the saucepan and cook over low heat, stirring constantly, for 2 minutes.
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Remove from the heat and add the softened gelatin.
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Stir until the gelatin melts, then stir in the chocolate until it melts completely.
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Let the mixture cool to room temperature, at least 2 hours.
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Once the chocolate has cooled, put the cream into the bowl of an electric mixer fitted with the whisk attachment.
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Whisk at medium speed until medium peaks form.
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(When you lift the whisk from the cream, a peak will form, and the very tip will fall back down.)
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Fold the cream into the chocolate mixture.
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To assemble the cake: Line an 8-inch square cake pan with plastic wrap, leaving a 10-inch overhang on all sides.
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Trim 1 inch from the long side of the cake to make a 12 x 16-inch rectangle.
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Invert the cake onto a large work surface and peel off the parchment paper.
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Cut a 4-inch-wide strip from one long side so that you have one 4 x 16-inch rectangle and one 8 x 16-inch rectangle.
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Cut both rectangles crosswise in half so that you end up with two 8-inch squares and two 4 x 8-inch rectangles.
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Put one of the 8-inch squares in the bottom of the cake pan.
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Spread half of the mousse on top, and arrange the 2 cake rectangles side by side on top of the mousse.
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Spread the remaining mousse on the rectangles, and top with the remaining cake square.
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Fold over the overhanging plastic wrap, cover with another sheet of plastic wrap, and refrigerate until set, at least 4 hours or up to 1 day.
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Once the cake is set, make the buttercream: Put the butter into the bowl of an electric mixer fitted with the paddle attachment and beat on medium-high speed until light and fluffy, about 2 minutes.
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Mix in the confectioners sugar and salt.
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Scrape down the sides and bottom of the bowl and add the coffee, condensed milk, and vanilla.
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Turn the speed to medium-high and mix until smooth and creamy, about 4 minutes.
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Invert the cake onto a cake platter and unwrap.
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Use an offset spatula or butter knife to spread the buttercream evenly over the entire surface of the cake.
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Refrigerate again to set the buttercream, at least 30 minutes.
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Serve chilled.
