Whisk the fat, 175 g brown sugar and salt with the whisk of the hand mixer for about 15 minutes until the sugar has dissolved. Stir in the eggs one by one. Mix flour, starch and baking powder and stir alternately with rum and 4 tablespoons lime juice into the egg mixture.
Grease a springform pan with a tube bottom insert (26 cm Ø) and dust with flour. Pour in the dough, smooth it down. Bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for 30-35 minutes.
Take out and let it rest in the mould for about 10 minutes. Turn over onto a cake rack. Prick cake all around and sprinkle with lime syrup. Let it cool down. Mix 2-3 tablespoons lime juice and icing sugar.
Dye with food colouring to a delicate green. Cover the cake with icing and let it dry. Sprinkle with 1 tablespoon each of pink and brown sugar and decorate with mint and lime skewers.