Preheat your oven to 350°F (175°C). Grease and line a cake pan with parchment paper.
In a bowl, sift together the all-purpose flour, cocoa powder, and baking powder. Set aside.
In a separate bowl, whisk the eggs and sugar together until pale and fluffy.
Gently fold the dry ingredients into the egg mixture until just combined.
Gradually add the melted butter and milk, continuing to fold until the batter is smooth.
Pour the batter into the prepared cake pan, spreading it evenly.
Bake in the preheated oven for about 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool in the pan for a few minutes.
Transfer the cake to a wire rack to cool completely before slicing and serving.