Beat the butter with the sugar. Separate the whites from the yolks. Add the yolks 1 by 1 to the butter. Continue beating.
Add the sifted flour, baking powder and cocoa. Add the milk and finally the beaten whites.
Mix the coconut flakes, cream and sugar in a bowl. Add the starch and stir until homogeneous.
Pour 1/2 the mixture into a suitable form, laid out with baking paper. Distribute the coconut mixture on top and cover with the remaining mixture.
Bake the cake at 338°F (170 °C) for about 30 min. Take it out and leave to cool. Optionally, sprinkle with powdered sugar and pour on a glaze of your choice.