Preheat oven to 350°F (175°C). Line a 9x9-inch baking pan with parchment paper.

Stir the espresso powder into the hot brewed coffee until completely dissolved. Set aside.

In a large bowl, add both sugars, yogurt, milk, oil, apple cider vinegar, and vanilla bean paste. Whisk until smooth.

In the same bowl, whisk together the cake flour, Dutch cocoa powder, natural cocoa powder, baking powder, baking soda, salt, and nutmeg, if using.

Add the hot coffee mixture and whisk for 30-45 seconds, until the batter is smooth, glossy, and slightly thickened.

Pour the batter into the prepared pan and smooth the top.

Bake for 35-40 minutes, checking at 35 minutes, until the center springs back when lightly touched, a toothpick inserted in the center comes out with a few moist crumbs, and the internal temperature reaches 208-210°F.

Let the cake cool in the pan for 5-8 minutes.

Make the warm mocha icing. Beat the butter until smooth and creamy.

Dissolve the espresso powder in 1 teaspoon of the milk until completely smooth.

Add the powdered sugar, Dutch cocoa powder, natural cocoa powder, vanilla bean paste, and dissolved espresso mixture. Beat on low until combined, then increase to medium-high just until mixed thoroughly. Do not overmix.

Add the remaining milk a little at a time until the icing is smooth and spreadable.

Microwave the icing in 5-second intervals, stirring between each, until it is smooth, glossy, and fluid enough to spread easily over the warm cake. It should look sun-warmed, not melted or greasy.

While the cake is still warm, use the handle of a wooden spoon or a thick skewer to poke holes evenly across the surface.

Spread the warm mocha icing evenly over the cake, encouraging it to seep into the holes and create a thin, fudgy layer.

Immediately sprinkle chopped dark chocolate and Maldon sea salt over the warm icing so they adhere to the surface.

Let the cake rest for 5-8 minutes so the icing can settle slightly into the cake.

Serve warm, or let cool completely if you prefer a firmer icing.