Special equipment: a N2O-charged whipped cream tank plus two charging cartridges
For the plum fool:, Melt the butter in a medium saucepan over medium-high heat. Add the sugar and cinnamon sticks, then stir in the plums and lemon juice. Reduce the heat to low and cook the plums until they are soft and have lost their shape, 5 to 7 minutes. Discard the cinnamon sticks and transfer the plum mixture to a blender. Blend until smooth, then pass the puree through a fine sieve set over a medium bowl. Cover the bowl with plastic wrap and set aside.
For the custard: In a medium saucepan bring the cream and milk to a boil over medium-high heat. In a medium heat-safe bowl, whisk the egg yolks and superfine sugar together. Pour the hot cream and milk into the bowl with the eggs and whisk to combine, then return the egg mixture to the saucepan and place over low heat. Gently cook the custard, stirring all the time, until the custard is thick enough to coat the back of a spoon, or reaches 180 degrees F on a cooking thermometer.
Pass the hot custard through a fine sieve set over a medium heat-safe bowl. Cover the surface of the custard flush with plastic wrap to prevent a skin from forming and refrigerate until completely chilled.
For the shortbread: Preheat the oven to 300 degrees F. Place the butter, flour and sugar together in a food processor and pulse until the mixture comes together. Add the pink peppercorns and pulse once more. Remove the mixture from the food processor and wrap in plastic wrap. Refrigerate the dough for 1 hour.
On a lightly floured work surface, roll the shortbread dough out to a 1/2-inch thickness. Cut into the shapes of your choice and place on a parchment-lined rimmed baking sheet. Bake the shortbread until it is dried across the surface and just cooked through, 35 to 40 minutes. Remove the shortbread from the oven and immediately sprinkle the demerara sugar over the top. Set aside to cool.
To serve: Mix 1 3/4 cups of the plum purée with the custard mixture. Pass the plum puree through a fine sieve and into a liquid measuring cup. Transfer the mixture to an N2O-charged whipped cream tank. Charge with two chargers, give it a good shake, and leave to settle for 10 to 15 minutes.
Divide a little of the leftover plum puree among serving bowls. Squirt the fool mix on top, sprinkle with pink peppercorns and serve with a piece of shortbread. Or let your guests serve themselves from the cream whipper for a fun party trick.