For the base
100 grams butter
1 medium banana (150 grams)
2 tablespoons desiccated coconut
50 grams instant vanilla pudding
250 grams ground cocoa biscuits
1 teaspoon dark rum
For the filling
750 ml coconut milk
60 grams cornflour (corn starch)
30 grams all purpose flour
100 grams sugar
50 grams desiccated coconut
150 grams butter
For the topping
150 grams dark chocolate
2 tablespoons vegetable oil
1 tablespoon unsweetened cocoa powder
First make the filling, because it takes a bit of time for it to cool down completely. Take out about 150 ml of the cold coconut milk and pour it over the mixture of cornflour sifted with all purpose flour, sugar and desiccated coconut and blend well. Bring the rest of the coconut milk to a boil over medium heat, and once it starts to boil, pour in the cornflour mixture you made (in a thin stream), whisking constantly with a wire whisk. Cook this for about 2-3 minutes, still whisking constantly, or until quite thickened. Cover the surface of this cream with plastic wrap and let it cool down completely.
To make the base, beat the butter with an electric mixer until light and fluffy, add the mashed banana and instant vanilla pudding and combine well. Add the rum and desiccated coconut and blend well, and then pour in the cocoa cookie crumbs (in a few additions), beating constantly on low. Lightly grease the bottom of a spring form pan (23 cm; 9") and press in the base batter evenly. Cover it with a piece of plastic wrap and let it sit at room temperature, not in the fridge.
When the filling is completely cool to the touch, beat the softened butter on high until light and fluffy, and then, beating constantly, add the cooked coconut cream, a tablespoon at a time, to the butter. The filling should be completely smooth and creamy when you've finished adding the coconut cream. Spread the filling evenly over the base and put the cake in the fridge for at least 2 hours.
For the topping, melt the chocolate with the oil in a double boiler or in the microwave, add the cocoa powder and whisk for a minute or two. Take the cake out of the fridge and quickly glaze the entire top surface with the chocolate glaze. Let the cake sit at room temperature for a few minutes, then put it in the fridge and let it sit there for at least 8 hours (preferably overnight) before serving.