For the base, melt butter and let it cool down a little. Put the "Oreos" and butter cookies in a freezer bag, close the bag. Run the cake roll over it, crumble the cookies. Mix with the butter. In a pie tin (24 cm Ø; 9.5 inches) press to the bottom, forming a rim. Chill for at least 30 minutes.
Break chocolate into pieces. Melt in a hot water bath and let it cool down briefly. Spread the chocolate on the pie base. Place in the refrigerator again for about 20 minutes.
For the filling, mix starch with approx. 50 ml coconut milk until smooth. Mix the remaining coconut milk with sugar, vanilla extract and 1⁄2 TL salt in a pot and bring to the boil. Stir in the coconut-starch-mix and simmer for about 1 minute while stirring. Remove the coconut pudding from the heat and let it cool down, stirring regularly (approx. every 5 minutes). Spread the pudding in the pie base and smooth it down. Chill for at least 4 hours (or overnight).
For the topping, roast the coconut chips in a pan without fat until golden brown, let them cool down. Whip the cream until stiff, stirring in icing sugar, rum and vanilla extract. To serve, spread on the pie and sprinkle with coconut chips.