Wash the lime with hot water, dab dry and finely grate the peel. Whisk the fat with the whisk of the hand mixer at the highest setting until white and frothy. Sprinkle in 100 g sugar. Stir in 2 eggs one after the other. Mix flour, baking powder and starch, sieve onto the fat mass and stir in. Add lime zest and 1 tablespoon of rum. Line the bottom of a springform pan (26 cm Ø) with baking paper. Fill in sponge mixture and smooth it down. Bake in the preheated oven (electric cooker: 175 °C/ gas: level 2) for 20-25 minutes. Cool down on a cake rack
Soak gelatine in cold water. Heat the pineapple and orange juice in a saucepan, add the remaining sugar. Add remaining rum, Triple Sec Curacao and Amaretto. Squeeze gelatine well and stir into the liquid. Beat the remaining eggs in a metal bowl over a hot water bath until foamy. Add warm (but not hot!!) liquid and whip briefly. Chill for 15-20 minutes, stirring continuously. Whip cream until stiff. When the liquid starts to set, fold in the whipped cream with a whisk
Place the cake ring around the cake base. Fill with cream and smooth it down. Chill for at least 3 hours. Remove the cake from the edge with a hot knife. Mix the pistachios and grated coconut and press to the edge. Decorate the cake with finely sliced pineapple, cocktail cherries, sliced lime, mint and paper umbrellas