Bring caster sugar, coconut milk, and desiccated coconut to a boil in a saucepan.
Stir in coconut cream, lemon juice, and coconut liqueur once sugar dissolves and leave to cool.
Whisk egg white until soft peaks form.
Fold the whisked egg white into the cooled coconut mixture.
Churn the mixture in an ice cream maker or freeze in a container until solid.
Preheat the oven to 200°C.
Melt and caramelize caster sugar over low heat in four ovenproof pans.
Remove from heat and stir a portion of butter into each pan.
Divide cubed mango among the pans.
Roll puff pastry to 5mm thickness and cut four circles slightly larger than the pans.
Cover each pan with a pastry circle and tuck the edges around the mango.
Bake for 15-20 minutes until golden-brown.
Grease a baking sheet with butter and caramelize more sugar in a frying pan.
Add chilli flakes and pour the caramel onto the sheet to harden.
Blend hardened caramel into fine crumbs using a food processor.
Melt crumb layers inside a 5cm ring on a silicone sheet to form four discs.
Turn each tatin out onto a plate and top with coconut sorbet and a chilli disc.