For the coconut sorbet, place the caster sugar, coconut milk and desiccated coconut into a saucepan and bring to the boil.
When the sugar has dissolved, remove from the heat and stir in the coconut cream, lemon juice and coconut liqueur. Set to one side and cool.
Place the egg white into a bowl and whisk until soft peaks form when the whisk is removed.
Fold the whisked egg white into the coconut mixture.
Pour the mixture into an ice cream maker and churn until frozen, according to manufacturer's instructions - or pour into a plastic box and freeze, removing the box from the freezer from time to time to stir.
For the mango tatin, preheat the oven to 200C/400F/Gas 6.
Divide the caster sugar among four small ovenproof blini pans (or small frying pans) over a low heat.
Cook, without stirring, until the sugar has melted and caramelised, turning golden-brown - take care as the sugar will be very hot.
Remove the pans from the heat and place a quarter of the butter into each pan. Stir gently to combine.
Divide the mango evenly among the four pans and keep warm, while you prepare the pastry.
Roll the puff pastry to 5mm/¼in thick on a clean, floured surface. Cut out four circles slightly larger than the circumference of the blini pans (or frying pans).
Cover each pan with a pastry round, pushing the edge down around the mango.
Transfer to the preheated oven and bake for 15-20 minutes, until the pastry is golden-brown and cooked through. Remove and allow to cool slightly.
For the chilli caramel crisp, lightly grease a baking sheet with butter. Place the sugar into a hot frying pan and cook until melted and caramelised, again taking care.
Remove the pan from the heat and add the chilli flakes. Pour the caramelised sugar onto the greased baking sheet and cool until hardened.
When hard, break into pieces and transfer to a food processor. Blend until fine crumbs are formed.
Place a non-stick silicone sheet onto a frying pan.
Place a 5cm/2in lightly greased chefs' ring onto the sheet and fill with enough of the caramel crumbs to make a thin layer. Heat until the caramel has liquefied; then remove from the heat and cool.
Carefully lift off the ring and allow the disc to cool totally. Repeat until you have four discs. Cool.
To serve, turn each tarte tatin out into the centre of one of four plates. Spoon any residual caramel around the tartes and top with a spoonful of the coconut sorbet and a chilli caramel disc for each serving.