Preheat the oven to 350 degrees and line a 6-inch round cake pan with parchment.
In a mixing bowl, whisk together the flour, sugar, black cocoa powder, baking powder, baking soda, and salt.
In a separate bowl or large measuring cup, combine the hot espresso, milk, oil, egg, and vanilla.
Pour the wet mixture into the dry ingredients and stir until the batter is smooth and no streaks remain.
Transfer the batter to the prepared pan and bake for 28 to 32 minutes, until a toothpick inserted in the center comes out with a few moist crumbs.
Let the cake cool in the pan for 10 minutes, then turn it out onto a wire rack to cool completely.
Place the chopped dark chocolate in a heatproof bowl. Heat the cream until it just begins to simmer, then pour it over the chocolate and let it sit for two minutes.
Stir the ganache until glossy and smooth, then spread it over the cooled cake.