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Put the raspberries and Champagne in a mini food processor or blender (or use a jug and a hand blender). Whizz until the purée is as smooth as you can get it, then use a wooden spoon or spatula to push as much of it through a sieve as you can. Discard the seeds left behind.
Put the cream and sugar in a saucepan and warm gently until the sugar melts. Increase the heat until just boiling, then boil vigorously for 2 1/2 mins, stirring constantly. Turn off the heat and stir in the raspberry-Champagne purée. Cool for 15 mins before dividing between 2 small pots or glasses. Chill for 30 mins, then sprinkle over the freeze-dried raspberry pieces and chill for at least 2 hrs more until set (or overnight if you’re making ahead).
To serve, remove the possets from the fridge and add some shortbread biscuits (shop-bought or find shortbread recipes here on bbcgoodfood.com).