Method

• 1.
  Arrange an oven rack in the centre position and preheat the oven to 325°F. Brush the bottom and sides of a 13 × 9-inch pan with a thin layer of oil. Line the bottom and two longer sides of the pan with a piece of parchment paper, leaving a bit of overhang and smoothing it to eliminate air bubbles
• 2.
  In a medium bowl, whisk together the flour, baking powder, baking soda, and salt to combine. Set aside.
• 3.
  In a separate medium bowl, whisk together the cocoa powder, coffee, and 2 tablespoons of the sugar until smooth. Set aside.
• 4.
  In a large bowl, with a hand mixer, beat the eggs and remaining 1 3/4 cups (12.3 oz / 350g) sugar on medium-low speed until combined, then increase the speed to high and beat until the mixture is thick, pale, and voluminous, about 3 minutes. Gradually add the mayonnaise, a few tablespoons at a time, beating constantly, and continue to beat until the mixture is smooth and well combined, about 2 minutes. Beat in the vanilla.
• 5.
  Reduce the mixer speed to medium-low and add about one-third of the dry ingredients, mixing just until the flour disappears. Stream in about half of the buttermilk and beat until incorporated, then add the remaining dry ingredients in two additions, alternating with the remaining buttermilk, and mix just until the last trace of flour disappears. Fold the batter several times with a flexible spatula, scraping the bottom and sides of the bowl to make sure it’s evenly mixed.
• 6.
  Pour half of the batter - about 4 cups (27.1 oz / 770g) if you want to be exact - into the bowl with the cocoa mixture and beat with the hand mixer on medium-low until the chocolate batter is streak-free.
• 7.
  Holding a bowl with each hand, alternate pouring the vanilla and chocolate batters into the prepared pan, layering them on top of each other. Scrape in every last bit of both batters, then drag a skewer or the tip of a paring knife through the pan, making figure eights, to swirl the batters together.
• 8.
  Bake until the surface of the cake is risen and light golden across the vanilla patches, and a cake tester or skewer inserted into the centre comes out clean, 40 to 45 minutes, rotating the pan front to back after 25 minutes. Let the cake cool completely in the pan.
• 9.
  In a small saucepan, combine the flour and salt and whisk to eliminate any lumps. Stream in the milk, whisking constantly, until you have a smooth, fluid mixture, then set the saucepan over medium-high heat and cook, whisking constantly, until the mixture is bubbling and thick and has the consistency of smooth mashed potato, about 3 minutes. Remove the saucepan from the heat and whisk in the vanilla. Scrape the mixture into a small bowl and press a piece of plastic directly onto the surface to prevent a skin from forming, then set the mixture aside to cool completely.
• 10.
  In a large bowl, with a hand mixer, beat the butter, cream cheese, and sugar on medium speed until smooth, then increase the speed to high and beat until the mixture is pale and light, about 3 minutes. Beating constantly, add the cooled flour mixture to the butter mixture a couple of tablespoons at a time, beating thoroughly after each addition. Once all of the flour mixture has been added, continue to beat until the sugar has completely dissolved (rub a dab between your fingers to check for any grit) and the frosting is nearly white and looks like whipped cream, about 4 minutes. If the frosting is a little bit loose and doesn’t hold a stiff peak, place the bowl in the refrigerator and chill, beating briefly with the hand mixer every 10 minutes, until it holds a stiff peak. Set the frosting aside.
• 11.
  Use a paring knife or small offset spatula to cut between the cake and the pan along the shorter sides. Invert the cake onto a wire rack, then lift off the pan and peel away the parchment paper. Reinvert the cake onto a serving platter (or a cutting board, if you don’t have a platter large enough for the cake). Scrape the frosting onto the cooled cake and spread across the surface and down the sides. Top with sprinkles.