1. To make the chocolate cake: Preheat the oven to 350°F. Spray an 11 × 17-inch rimmed baking sheet with nonstick cooking spray, line with parchment paper, and spray the paper. Set aside.

2. Sift the cocoa, flour, and cornstarch together and set aside.

3. Put the egg whites in the bowl of an electric mixer fitted with the whisk attachment and whisk at medium-high speed until frothy. With the machine running, slowly add 1/3 cup of the sugar and continue whisking until medium-soft peaks form. (When you lift the whisk from the mixture, a peak will form and the top of the peak will fall back down.) Transfer the whipped whites to a large bowl.

4. Put the yolks in the electric mixer bowl and whisk on medium speed until the yolks break. With the machine running, add the salt and the remaining 1/3 cup sugar in a slow, steady stream. Continue whisking until the mixture is pale yellow, thick, and doubled in volume, about 12 minutes.

5. 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. Add the remaining whites to the mixture and fold gently until only a few white streaks remain. Whisk the oil and buttermilk together until smooth and homogenous, then fold into the batter until completely incorporated.

6. Spread the batter evenly in the baking sheet. Bake for 5 minutes, then rotate the pan and bake until a tester comes out clean, about 5 more minutes. Cool completely in the pan on a rack.

7. Meanwhile, make the mousse: Put the milk, sugar, and salt in a small saucepan, stir well, and set over medium heat. Warm just until bubbles form around the edges, then whisk in the Horlicks until completely dissolved. Remove from the heat.

8. Put the yolks in a large mixing bowl and whisk until the yolks break. Add the warmed Horlicks mixture in a steady stream while whisking constantly. Return the mixture to the saucepan and cook over low heat, stirring constantly, for 2 minutes. Remove from the heat and add the softened gelatin. Stir until the gelatin melts, then stir in the chocolate until it melts completely. Let the mixture cool to room temperature, at least 2 hours.

9. Once the chocolate has cooled, put the cream into the bowl of an electric mixer fitted with the whisk attachment. Whisk at medium speed until medium peaks form. (When you lift the whisk from the cream, a peak will form, and the very tip will fall back down.) Fold the cream into the chocolate mixture.

10. To assemble the cake: Line an 8-inch square cake pan with plastic wrap, leaving a 10-inch overhang on all sides. Trim 1 inch from the long side of the cake to make a 12 × 16-inch rectangle. Invert the cake onto a large work surface and peel off the parchment paper. Cut a 4-inch-wide strip from one long side so that you have one 4 × 16-inch rectangle and one 8 × 16-inch rectangle. Cut both rectangles crosswise in half so that you end up with two 8-inch squares and two 4 × 8-inch rectangles.

11. Put one of the 8-inch squares in the bottom of the cake pan. Spread half of the mousse on top, and arrange the 2 cake rectangles side by side on top of the mousse. Spread the remaining mousse on the rectangles, and top with the remaining cake square. 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.

12. 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. Mix in the confectioners’ sugar and salt. Scrape down the sides and bottom of the bowl and add the coffee, condensed milk, and vanilla. Turn the speed to medium-high and mix until smooth and creamy, about 4 minutes.

13. Invert the cake onto a cake platter and unwrap. Use an offset spatula or butter knife to spread the buttercream evenly over the entire surface of the cake. Refrigerate again to set the buttercream, at least 30 minutes. Serve chilled.