Heat the sugar and water in a saucepan until dissolved then boil the syrup until the mixture reaches the soft ball stage, 100C/220F (use a sugar thermometer to measure this).
Place the ground almonds, egg white and almond extract into a bowl. Pour over the sugar syrup and mix vigorously until the mixture forms a thick paste. Chill the marzipan mixture in the fridge for 1-2 hours, or until firm.
Meanwhile, preheat the oven to 210C/425F/Gas 7.
Roll the puff pastry out thinly on a floured surface. Cut out 4 x 12cm/5in circles, place onto a baking tray and score the centre of each circle with a knife. Brush each pastry circle with the beaten egg.
Roll the chilled marzipan out to 0.5cm/¼in thick. (If the marzipan is too hard to rollout, allow it to warm slightly at room temperature.) Cut out 4 x 11cm/4in circles and place each circle on top of a pastry circle.
Arrange the raspberries in concentric circles on top of each circle of marzipan so that all of the marzipan is covered. Sprinkle over the flaked almonds.
Transfer to the oven to bake for 15-18 minutes, or until the pastry is risen and golden-brown. Remove the tarts from the oven and dust with icing sugar immediately.
Meanwhile whisk the double cream in a bowl until stiff peaks form when the whisk is removed. Whisk in the icing sugar and vanilla extract.
For the raspberry purée, blend the raspberries and icing sugar in a food processor to a purée. Sieve the sauce into a bowl.
To serve, spoon some of the raspberry purée onto each of 4 serving plates and top with a tart. Top with a quenelle of the vanilla cream.
