For coconut base, preheat oven to 180C. Combine flour, coconut, brown sugar, a pinch of salt and 40gm melted butter in a bowl, spread on an oven tray lined with baking paper and bake, stirring occasionally, until evenly golden (6-8 minutes), then set aside to cool. Process in a food processor with remaining butter to combine, then press into the base of a 23cm-diameter spring-form cake tin buttered and lined on the base with baking paper and bake until golden (8-10 minutes).
Meanwhile, process cream cheese and sugars in a food processor until smooth, add eggs one at a time and process to combine. Add coconut cream, lime rind and juice and vanilla seeds, process to combine. Pour over coconut base, reduce oven to 160C and bake until light golden and set around edges with a slight wobble in the centre (25-30 minutes). Cool to room temperature then refrigerate until completely chilled (2-3 hours).
Meanwhile, for candied coconut, remove brown skin from coconut flesh with a peeler (discard) and peel flesh into strips, then combine in a saucepan with sugar and shake pan occasionally over medium-high heat until liquid leaches from coconut (1-2 minutes). Reduce heat to low, shake pan occasionally until mixture is dry but not coloured (8-10 minutes), spread on a tray lined with baking paper and cool completely.
Meanwhile, for brown sugar pineapple, spread half the sugar in the base of a large frying pan, add half the pineapple in a single layer and cook over medium-high heat, turning occasionally, until sugar melts and pineapple caramelises (3-4 minutes). Transfer pineapple to a tray, strain syrup into a bowl, wipe out pan and repeat with remaining sugar and pineapple. Add lime juice to syrup and refrigerate pineapple and syrup separately until chilled. Serve cheesecake topped with brown sugar pineapple, drizzled with syrup and scattered with candied coconut.