Preheat your oven to 350°F (175°C) and prepare an 8-inch cake pan by lining it with parchment paper and greasing the sides.
In a large mixing bowl, whisk together the granulated sugar, unsweetened cocoa powder, and salt until fully combined and lump-free.
Stir in the melted butter, then add the eggs one at a time, followed by the vanilla extract and hot water with espresso powder if using. Mix until smooth and glossy.
Pour the batter evenly into the prepared pan and gently smooth the top with a spatula.
Bake for 25 to 30 minutes, or until the edges are set but the center still looks slightly soft and a toothpick inserted near the edge comes out mostly clean.
Let the cake cool in the pan for 10 minutes, then carefully run a knife around the edges to loosen and invert it onto a cooling rack.
Allow it to cool completely, then flip it right-side-up onto a serving plate and chill before serving for best texture.
Notes
Nutrition information is automatically calculated, so should only be used as an approximation.