For the rough puff pastry, place the flour in a mound on the work surface and make a well in the centre.
Place the butter and salt into the well and work them together with the fingertips of one hand, gradually drawing the flour into the centre with the other hand.
When the cubes of butter have become small pieces and the dough is grainy, gradually add the iced water and mix lightly until it just comes together. Form the pastry into a ball, flatten slightly, wrap in cling film and refrigerate for 20 minutes.
Flour the work surface and roll out the pastry into a 40cm/16in x 20cm/8in rectangle.
Fold it into three like a business letter and give it a quarter-turn.
Roll the block of pastry out as before, and fold it into three again.
These are the first two turns - wrap the block in cling film and refrigerate it for 30 minutes.
Give the chilled pastry another two turns, rolling and folding as before.
Wrap the pastry in cling film and refrigerate for at least 30 minutes before using.
Meanwhile, for the tart filling, place the sugar and water into a saucepan and bring to a gentle simmer, stirring continuously until the sugar has dissolved.
Bring the syrup to the boil and cook until it reaches110C/220F when measured with a sugar thermometer (this is the soft ball stage).
Place the ground almonds into a bowl along with the egg white and almond extract.
Pour on the sugar syrup and mix vigorously to form a thick paste. Then set aside in the fridge until completely cold.
Preheat the oven to 210C/425F/Gas 7.
Roll the rough puff pastry to a thickness of 3mm/1/8in. Cut out four 12cm/4½in circles and transfer to a baking sheet.
Lightly score the centre of the pastry with a knife then brush with beaten egg.
Dust the work surface with icing sugar, then roll the marzipan out to a thickness of 5mm/¼in. Cut four 11cm/4in circles and place in the centre of the pastry.
Cover the marzipan with the plum slices, tightly overlapping, in a circle.
Place in the oven and bake for 15-18 minutes until the pastry is risen and golden-brown.
Meanwhile, for the star anise caramel, place the sugar and star anise into a frying pan and cook, without stirring, until the sugar has melted and is just golden brown.
Whisk in the butter and double cream (CAUTION: the mixture will be extremely hot. You may want to wear an oven glove) and bring to a simmer.
Cook for 3-5 minutes until just thickened then pass through a fine sieve into a clean pan.
To serve, place the tart in the centre of a small plate and spoon the sauce around the edge. Finish with a spoonful of ice cream in the centre of the tart.