Open the coconut, shave the white flesh on a grater and pour lukewarm water. Let the liquid soak for a while. Beat the eggs with the sugar until creamy and add the coconut and the resulting coconut milk. Pour the mixture into a buttered shallow gratin dish and bake for 15 min at 220 °C until the surface is lightly browned.
Turn the pudding out onto a plate and serve with the compote and cookies.