Preheat the oven to 190°C/170°C fan/375°F/gas 5.
Brush the base of a standard 26cm (10½in) quiche dish with some of the melted butter.
Lay the filo pastry sheets flat on the worktop. Take one sheet at a time and gather together. Roll the first sheet into a rose and place in the middle of the baking dish. Follow with the rest of the filo sheets to completely cover the dish.
Scatter the mango in between the filo sheets, gently pushing them in place. Generously brush the pastry with the rest of the melted butter, covering every possible crevice.
In a small bowl, mix together the cinnamon and icing sugar, then dust half over the filo tart and bake in the oven for 20 minutes.
Meanwhile, make the coconut custard. In a saucepan over a medium heat, bring the coconut milk, double cream and vanilla pod to the boil. In a large bowl, whisk together the egg yolks and sugar to combine. While continually whisking, carefully pour the hot coconut milk and cream into the eggs and sugar. Once combined, pour the mixture back into the saucepan and return to the heat.
Cook the custard, stirring occasionally, until just before it reaches boiling point, the custard has thickened and coats the back of a wooden spoon. The custard should read 82°C (180°F) on a kitchen thermometer, if using. Strain the custard through a sieve, discard the vanilla pod, cover and set aside until ready to serve.
Pour the coconut custard over the tart. Return to the oven and bake for another 20 minutes.
Remove from the oven and set aside to cool for 15 minutes. Sprinkle over the lemon thyme leaves, then dust with the remaining cinnamon sugar before slicing to serve.
