Preheat your oven to 350°F. Grease a 17×11-inch rimmed baking sheet and line it with parchment paper.
In a medium saucepan, combine the cubed butter, water, and cocoa powder. Heat over medium-low, whisking occasionally until the butter has melted and the mixture is smooth—avoid boiling. Once smooth, remove from the heat and let cool until just warm, about 15 minutes.
Meanwhile, in a large mixing bowl, whisk together the flour, packed light brown sugar, espresso powder (if using), baking soda, and salt. If there are any clumps of sugar, break them up using your fingers until the dry mixture is smooth. Create a well in the center.
In a separate bowl or a large measuring cup with a pour spout, whisk together the buttermilk, eggs, and vanilla extract. Slowly add the buttermilk mixture into the slightly cooled cocoa mixture in the saucepan, whisking constantly to combine.
Pour the wet ingredients into the dry mixture and beat until smooth and fully incorporated. Scrape down the sides of the bowl and mix briefly again to ensure everything is well blended.
Pour the batter into the prepared baking sheet, spreading it evenly. Tap the pan on the counter a few times to release air bubbles and level the batter.
Bake for 18–20 minutes, or until a toothpick inserted into the center comes out clean. The cake should slightly pull away from the pan’s edges, but if it doesn't, run a knife along the sides. Let the cake cool completely in the pan.
Once cooled, transfer the cake to the freezer until it’s firm—at least 30 minutes, or overnight if desired.
When firm, invert the cake onto a clean work surface. If it sticks to the pan, allow it to sit at room temperature for 5 minutes, then try again. Remove and discard the parchment paper. Trim the cake into three equal 11×5-inch rectangles. (There will be leftover scraps—perfect for snacking!) Cover the layers in plastic wrap while you prepare the fillings.