Mix soft butter and sugar thoroughly with a hand mixer. Beat until it is airy and without lumps.
Add the eggs one at a time - beating well between each addition. Beat until the mixture is light, airy, and creamy.
In a bowl, mix together flour, baking powder, cocoa, and vanilla sugar.
Sift the flour mixture into the batter alternating with the addition of milk. Combine the batter with a spatula, avoiding beating, as this will make the cake tough and rubbery.
Pour the batter into a small baking pan (approximately 25 x 30 centimeters) that is greased with butter or lined with parchment paper.
Bake the cake at the bottom of the oven at 175 degrees Celsius (347 degrees Fahrenheit) for about 40 minutes. Check if it is baked through by sticking a wooden skewer into the center of the cake. If the skewer comes out clean, the cake is done. If there is raw batter on it, bake it a bit longer.