Cut both pineapples in half from the top and remove the hard centre part: the heart is not very tasty. Put the four halves on the grill of The Bastard and cook for at least 2 hours at a low temperature. Remove the pineapple from The Bastard and cut off the skin. When the pineapple halves are cooled, cut them into slices as thin and straight as possible. Keep the unsuccessful pieces or eat them straight away. Mix the cream cheese with sugar, lime juice and rind and the mango in a food processor until smooth. Clean the strawberries, pluck off the crown and cut them into nice, thin slices, just like the pineapple. Line a cake tin with plastic foil, letting it extend well over the edges so that you can make a firm package of it later on. Start with a layer of pineapple, then the mango mixture and finally a layer of strawberries. The first layer will soon be the top, so make sure it is completely closed. Repeat this until you reach the edge of the mould and close with pineapple. Wrap it up well with the plastic foil, so that you have a nicely shaped package. Put it in the freezer for 3 hours (but preferably overnight) and place some weight on it (for example a packet of milk). This is to get the excess moisture out of the ice cream cake; the less moisture, the easier it is to cut. Once the ice cream cake is completely frozen, pour off the excess juice, place a plate or cutting board on the cake tin and quickly turn it over. With a sharp knife, cut off the uneven edges and serve in slices.