Heat the oven to 350 °F and grease a 10x15 baking pan well. The batter spreads thin, so a fully greased pan helps the cake release cleanly from edge to edge.

Whisk the flour, sugar, baking soda, and salt together in a large mixing bowl, then set the bowl aside. Mixing the dry ingredients first helps the leavening and salt distribute evenly through the batter.

Melt the butter in a small saucepan, stir in the cocoa powder and black coffee or water, and bring the mixture to a boil over medium-high heat. Before it boils, it should look glossy and fluid, and once it bubbles the cocoa aroma should smell noticeably deeper.

In a small bowl, mix the buttermilk, eggs, and vanilla extract until smooth. Blending these together first helps the eggs combine quickly when they meet the warm chocolate mixture.

Pour the hot cocoa mixture into the dry ingredients and stir to combine, then add the buttermilk mixture and whisk for 1 minute. Work steadily so the warm batter stays smooth, and stop when it looks silky and evenly mixed.

Spread the batter in the prepared pan and bake for 20-22 minutes. The cake is done when the center looks matte and slightly puffed and a toothpick inserted in the middle comes out clean.

Sift the powdered sugar and cocoa powder into a large mixing bowl. This extra step prevents tiny dry lumps that stay stubborn in warm icing.

Warm the milk, butter, and salt in a small saucepan until the mixture reaches a simmer, then remove it from the heat and stir in the vanilla extract. The butter should be fully melted and the surface should look smooth, not greasy or separated.

Pour the hot milk mixture over the sifted sugar and cocoa, then stir with a spoon until smooth. Use a spoon rather than a whisk so the icing stays glossy and does not fill with little air bubbles.

Let the icing stand for 5 minutes, stirring now and then, then pour it over the warm cake. It should look like fluid fudge at this point and spread easily without running too thin.

Leave the cake at room temperature until the icing firms enough to slice neatly. Within about five minutes, the top should begin to lose some shine and start forming that classic delicate crust.

Once the cake is cool, cover it and keep it at room temperature. The icing stays at its best when the cake is protected from air and not stacked under tight wrap that can mark the surface.