Bring coconut milk and 200 ml milk to the boil in a saucepan. Mix the remaining milk with egg yolks, sugar and starch. Stir the mixture into the hot milk and let it simmer for about 2 minutes while stirring. Pour into a flat dish and cover the pudding directly on the surface with foil.
Allow to cool until the pudding is at room temperature.
Peel the mango and cut the flesh from the stone. Cut the flesh into small pieces and puree finely with a blender. Whip butter and icing sugar with the whisk of the hand mixer until creamy white.
Stir in the pudding bit by bit.
Place baking paper on a board and place the butter biscuits on it in a rectangular shape (4 x 5 biscuits) close together. Place a rectangular cake frame around it and tighten it firmly.
Spread approx. 1/4 cream on the biscuits, sprinkle with approx. 1/4 grated coconut and spread approx. 1/3 mango puree. Layer the remaining biscuits, cream and grated coconut on top of each other. Spread the remaining cream on the last layer of biscuits and sprinkle with the remaining grated coconut.
Chill for about 2 hours. Carefully remove from the frame and cut into pieces.