Instructions

1. Make the pastry cream: To a small deep pot, add the milk, sugar, vanilla, nutmeg, and salt. In a small bowl, whisk together the cornstarch and egg yolks until smooth. To a large bowl, add the butter and place a fine-mesh strainer on top. 
2. Bring the milk mixture to a simmer over medium heat, whisking frequently, 3–4 minutes. When it begins to simmer, ladle about ¼ cup of the hot liquid into the egg mixture and whisk to combine. Pour the egg mixture into the pot and whisk vigorously until the pastry cream bubbles and comes to a boil. Allow it to boil for about 30 seconds, then turn off the heat and whisk in the bourbon, brandy, and rum.
3. Using a silicone spatula, press the pastry cream through the strainer into the bowl with the butter. Whisk until the butter is fully incorporated. Place a piece of plastic wrap directly on the surface of the pastry cream to prevent a skin from forming, then set aside to cool to room temperature. Refrigerate for at least 6 hours, or up to 24.
4. Make the cake: Position a rack in the center of the oven and preheat to 325°F. Line a 13- by 18-inch rimmed baking sheet with parchment. Grease with nonstick spray and set aside. 
5. In a large bowl, whisk together the sugar and eggs until pale yellow and fluffy, about 2 minutes. Add the oil about ¼ cup at a time, whisking to fully emulsify into the egg mixture before adding more. Whisk in the vanilla.
6. In a medium bowl, whisk together the flour, nutmeg, salt, baking powder, baking soda, and cinnamon, then whisk the flour mixture into the egg mixture until fully incorporated. Add the milk and whisk until combined and a thin batter forms.
7. Scrape the batter onto the prepared baking sheet and smooth into an even layer. Bake until the cake is set and very light golden brown around the edges, 25–30 minutes. Transfer to a heatproof surface and set aside to cool. 
8. Meanwhile, make the soak: In a heatproof bowl, combine the sugar and ¼ cup of boiling water. Add the bourbon, brandy, and rum, and whisk until the sugar has dissolved.
9. Invert the cake onto a large cutting board. Peel off and discard the parchment. Using a serrated knife, cut the edges of the cake, removing about ¾ inch on all sides, to create a perfect, clean rectangle. Cut the cake into three even rectangles, each measuring about 13 by 5 inches. Place one rectangle on a large serving platter. 
10. Using a pastry brush, brush the first cake layer with some of the soak. Pour half of the pastry cream on top of the first cake layer and smooth it out, leaving a ½-inch border. Place another rectangle of cake on top, brush with the soak, and cover with the remaining pastry cream. Top with the final piece of cake and brush with more soak. Cover the cake with plastic wrap, pressing it directly on all sides of the cake to make a tight package. Refrigerate for at least 6 hours, or up to 24. 
11. Make the meringue: In a stand mixer fitted with the whisk attachment, beat the egg whites on high until foamy and soft peaks form, about 2 minutes. Turn the mixer to medium-high and add the sugar 2 tablespoons at a time, waiting about 45 seconds between each addition to add more. Once all the sugar is incorporated, continue beating until the meringue is smooth, glossy, and holds stiff peaks, about 2 minutes more.
12. Retrieve the cake from the fridge and, using an offset spatula, cover the cake with the meringue, creating dramatic swooshes and tufts, aiming for plenty of height. Using a kitchen blowtorch, toast the meringue all over until golden brown, 2–3 minutes. Serve immediately.