Preheat the oven to 175°C (350°F). Grease a 9×13 inch baking pan and lightly dust it with flour. Melt 225 g of butter together with 75 g of cocoa powder and 160 ml of water in a saucepan over medium heat. Take it off the heat and let it cool for a few minutes.
Beat 2 eggs with 240 ml of buttermilk and 2 teaspoons of vanilla extract in a bowl. Stir in the cooled butter-cocoa mixture until it is well blended.
Sift 250 g of flour, 400 g of sugar, 1 teaspoon of baking soda, and 1 teaspoon of salt into another bowl. Carefully fold the dry ingredients into the wet mixture until the batter is smooth and uniform.
Pour the batter into the prepared pan. Bake for 35–40 minutes. Test the center with a toothpick; it should come out clean. Allow the cake to cool completely on a rack.
For the icing, melt 115 g of butter over low heat. Stir in 15 g of cocoa powder. Remove from heat and whisk in 450 g of powdered sugar and 90–120 ml of buttermilk until smooth. Add 1 teaspoon of vanilla extract. Adjust the amount of buttermilk until the icing reaches the consistency you want.
Spread the icing over the cooled cake. Cut into squares and serve. Store any leftovers in an airtight container for 2–3 days.