Heat the oven to 350°F (180°C). Grease a 9x13-inch baking pan, then line the bottom with parchment paper to make it easier to remove the cake later.
In a large mixing bowl, stir together the cocoa powder and boiling water until smooth. Let it sit for a minute or two to cool slightly.
Add the butter, sugar, eggs, flour, baking powder, salt, and milk to the cocoa mixture. Use an electric mixer to blend everything until you have a smooth batter.
Pour the batter into the prepared baking pan and spread it evenly with a spatula. Bake for 35–40 minutes or until the edges pull away from the sides of the pan and the top springs back when you lightly press it with your finger.
Let the cake cool in the pan for about 10 minutes, then carefully turn it out onto a wire rack. Peel off the parchment paper and let it cool completely.
Warm the apricot jam in a small saucepan over low heat until it’s thin and easy to spread. Brush it evenly over the cooled cake.
To make the icing, melt the chocolate and water together in a saucepan over low heat. Stir until smooth and glossy. Let it cool for a couple of minutes, then mix in the confectioners’ sugar and sunflower oil until the icing is silky and spreadable.
Pour the icing over the cake and spread it gently with an offset spatula. Let it set for about 30 minutes until firm.
Finish by decorating with chocolate curls, then slice into 16 pieces and enjoy!