Preheat the oven (electric cooker: 175 °C/recirculating air: 150 °C/gas: see manufacturer). Grease a square springform pan (24 x 24 cm; alternatively round, 26 cm Ø). For the dough, whisk 200 g butter and 200 g sugar until creamy.
Stir in the eggs one by one. Mix flour and baking powder. Stir into the egg-sugar mixture. Smooth the dough in the tin. Pre-bake in a hot oven for about 20 minutes.
For the compote, boil up lime juice and blueberries with juice. Mix starch with 2 tablespoons of water until smooth, stir into the berries. Simmer for about 2 minutes.
For the icing, mix the grated coconut, 40 g sugar and double cream. Take the springform pan out of the oven and spread the berry compote on the bottom. Add the coconut icing loosely.
Bake at the same temperature for about 15 minutes. Remove from the oven and leave to cool in the mould. Remove the cake from the edge of the tin with a knife. In about 35