Preheat the oven to 170°C/340F. Grease and line a regular-sized loaf tin with baking paper that has overhangs allowing for easy removal of the cake once baked.
In a large mixing bowl, combine the hot water, cocoa, butter, and espresso powder. Whisk until all the butter is melted and the cocoa powder is incorporated with no lumps.
125 grams water, 1 teaspoon espresso powder, 40 grams unsweetened cocoa powder, 60 grams butter
Add in the eggs, yogurt, and vanilla. Whisk together until well combined.
2 teaspoons vanilla extract, 55 grams Greek yogurt, 2 large eggs
Add the flour, baking powder, baking soda, salt, and sugar. Whisk until well combined.
180 grams plain flour, ½ teaspoon table salt, 2 teaspoons baking powder, ¼ teaspoon baking soda, 200 grams white granulated sugar
Pour the cake batter into the prepared tin and bake for 35 to 45 minutes. The cake is done with a cake tester or toothpick and comes out mostly clean.
Allow the cake to cool in the tin for 10 to 15 minutes before lifting it out and allowing it to cool completely on a wired cooling rack.
In a small mixing bowl, combine the icing sugar, melted butter, vanilla, and 2 tablespoons of warm water. If the icing is too thick, add warm water 1 tablespoon at a time, mixing in between each addition until a thick pourable consistency is achieved.
115 grams icing sugar, 15 grams unsweetened cocoa powder, ½ teaspoon vanilla extract, 30 grams butter, 2-4 tablespoons warm water
Pour the icing glaze over the cooled cake, allowing it to drip down the sides of the cake. Let the icing set a bit, slice, serve and enjoy!