For the base, mix fat, sugar, vanillin sugar and rum flavouring until creamy. Stir in the eggs one after the other. Mix flour, 50 g grated coconut and baking powder and add to the egg mixture together with the milk and stir well.
Put the dough into a greased and breadcrumbed springform pan (26 cm Ø) and smooth it down. Bake in the preheated oven (electric: 200 °C/ gas: level 3) for 18-20 minutes.
Remove the base from the springform pan and let it cool down. Soak the gelatine in cold water. Peel the Charantais melon, cut in half and remove the seeds. Cut off 10 slices, puree the remaining flesh.
Add 50 g sugar and lime juice. Stir in mascarpone. Dissolve gelatine over low heat and stir into the melon cream. Leave to set a little in the fridge. Whip cream until stiff and fold into the cream.
Place a springform pan rim around the base, spread melon cream on top and leave to set in the fridge for 2 hours. Halve and seed the Galia melon. Unscrew the flesh with a ball cutter.
Spread melon slices and melon balls on the cake. Mix the cake glaze powder and 2 tablespoons of sugar in a pot. Gradually stir in 250 ml water. Bring to the boil while stirring. Let the icing cool down for about 1 minute and pour over the melons.
Refrigerate for another 2 hours. Roast the remaining grated coconut in a pan without fat until golden brown and sprinkle the cake with it. Cream tastes good with it. Makes about 12 pieces.