Preheat the oven to 350°F (180°C) and lightly grease an 8"x8" pan.
In a large bowl, mix sugar, flour, cocoa, espresso powder, and baking powder. Add coconut oil, plant-based milk, and vanilla, and stir gently. Spread the batter evenly into the pan.
In a separate bowl, mix white sugar, brown sugar, and cocoa powder for the middle layer.
Sprinkle the powder mixture evenly over the cake batter and gently shake the pan to spread it evenly.
Pour hot water over the top without mixing; it should look like a puddle.
Bake for 30-35 minutes until the center is almost set.
Let the cake cool for 15 minutes before serving.
Enjoy warm with a scoop of dairy-free ice cream, if desired!