Melt salted butter in a pan with sugar and cinnamon sticks.
Add plums and lemon juice, then cook on low heat until softened.
Remove cinnamon, blend plums until smooth, and sieve into a bowl.
Boil double cream and milk in a saucepan.
Whisk egg yolks and caster sugar, then pour the hot liquid over them while whisking.
Return mixture to the pan and cook on low heat until thickened to 82°C.
Sieve the custard into a bowl and chill in the fridge.
Preheat the oven to 150°C.
Pulse butter, sugar, and flour in a food processor until combined.
Add pink peppercorns, pulse again, and chill the dough for one hour.
Roll dough to 1cm thickness and cut into shapes.
Bake on a lined tray for 35 to 40 minutes.
Sprinkle with demerara sugar and leave to cool.
Mix 400g of plum purée with the chilled custard.
Sieve the mixture into a cream whipper and charge with two gas chargers.
Shake well and let settle for 10 to 15 minutes.
Serve the fool with leftover purée, pink peppercorns, and shortbread.