Line a cake tin (approx. 26 cm) with baking paper. Beat the eggs and sugar for approx. 5 mins. using the whisk on a hand mixer. Melt the butter, mix with the rum and flour, transfer the mixture to the tin.
For approx. 25 mins. in the centre of an oven preheated to 180°C. Allow to cool a little on a rack, cut crosswise into five slices approx. 4 cm wide.
Icing & decoration
For the icing, roughly chop the chocolate, melt on a low heat with the butter and icing sugar, pour the mixture over the slices. Sprinkle with the coconut flakes, leave to dry.