For the preserved fruit, prepare your preserving jars by washing them in hot soapy water. Sterilise the jars and a knife by washing them in the dishwasher. Keep them warm in the oven until you’re ready to fill them.
Add the sugar and 400ml/14fl oz water to a pan and heat gently, stirring until the sugar dissolves. Bring to a boil, stop stirring and boil for 1-2 minutes. Turn off the heat and work quickly so that the syrup doesn’t cool too much.
Fill the sterilised jars with plums and pour the hot syrup on top, leaving 2.5cm/1in of space at the top of the jar. Run a sterilised knife between the fruit and the edge of the jar to remove any air bubbles.
Wipe the rims with a clean cloth and screw on the lids. Place the jars in a deep pan and cover with cold water. Turn on the heat and bring to a boil. Cook for 20 minutes in boiling water, then turn off the heat and leave to cool in the pan.
If the canning process has been successful the lid should be concave and not spring back when pressed in the centre. Store the preserved fruit in a cool, dark place. Unopened jars should keep for a year; opened jars will keep for around three weeks in the fridge.
For the sweet shortcrust pastry, sift together the flour and icing sugar in a mixing bowl. Tip in the cubes of butter and rub with your fingers until the mixture resembles breadcrumbs.
Add the egg yolk and work together with your hands, adding a little ice cold water if necessary to bring the pastry together. Wrap in cling film and leave to rest in the fridge for at least 10 minutes.
This amount of pastry is enough for two tarts, so keep half in the fridge or freezer to use another time.
Preheat the oven to 180C/350F/Gas 4.
Remove the pastry from the fridge and roll out on a floured surface into a large circle, as thin as possible, about 2-3mm thick. Carefully place the pastry over the tart tin and press down with a rolling pin to trim the edges. Gently push the pastry into the ridges and chill until needed
For the frangipane, beat the butter and sugar together using an electric mixer or hand mixer, until light and fluffy. Beat in the egg and then fold in the ground almonds
Spoon the frangipane into the pastry case and smooth over the top. Bake for 30-40 minutes, or until the filling has puffed up and the pastry is crisp.
Drain the preserved plums, reserving the liquid. Cut each half in three wedges and arrange over the top of the baked tart.
Place the preserving liquid in a small saucepan and bring to a boil. Boil for two minutes, or until the volume of liquid has reduced by half. Remove from the heat and cool slightly. Brush the reduced preserving liquid over the tart to glaze.