Heat the oven to 350°F (175°C). Grease an 8-inch square baking pan and line the bottom with parchment, leaving a little overhang if you want to lift the cooled cake out easily.

Whisk the sugar, flour, cocoa powder, baking soda, and salt together in a large bowl. Break up any cocoa lumps so the finished batter will be smooth.

In a separate bowl, whisk the room-temperature egg, buttermilk, melted and slightly cooled butter, and vanilla extract until blended. The butter should not be hot enough to cook the egg.

Pour the wet mixture into the dry ingredients and stir just until no large dry patches remain. Avoid prolonged mixing, since overworking the batter can make the cake less tender.

Add the hot coffee or hot water and whisk gently until the batter is smooth. The mixture will be fairly thin, which is expected and helps create a moist crumb.

Pour the batter into the prepared pan and bake for 28 to 35 minutes. The cake is ready when the center springs back lightly and a toothpick comes out with a few moist crumbs.

Cool the cake in the pan for 15 to 20 minutes, then continue cooling until completely cold. For the cleanest slices and firmest cold-cake texture, refrigerate the covered cake for 1 to 2 hours before cutting.

For the optional topping, whisk the confectioners' sugar, cocoa powder, melted butter, vanilla, and salt together with enough milk to make a spreadable glaze. Spread it over the fully cooled cake, then chill briefly before slicing if desired.