Preheat oven to 180°C. Grease a 22cm x 32cm rectangular slice pan; line base and long sides with baking paper, extending the paper 5cm over the sides.
Beat butter and sugar in a small bowl with an electric mixer until pale and fluffy. Beat in eggs, one at a time, until just combined after each addition. Transfer mixture to a large bowl; stir in desiccated coconut, sifted flour, coconut cream and pineapple, in two batches, until combined. Spread mixture into pan.
Bake slice for 45 minutes or until a skewer inserted into the centre comes out clean. Leave in pan for 10 minutes before transferring to a wire rack to cool completely.
Make lime glaze icing. Sift icing sugar into a small heatproof bowl; stir in butter and enough of the juice to make a soft paste. Place bowl over a small saucepan of simmering water; stir until icing is spreadable. Working quickly, spread icing over cake; sprinkle with shredded coconut.