Roll out the pastry on a lightly floured surface and use to line a 23 cm (9 inch) loose-bottomed flan tin. Spread half the plum conserve or jam over the base.
Beat the butter and sugar together in a large bowl with a hand-held electric whisk until pale and fluffy. Gradually beat in the eggs, then stir in the ground almonds, almond extract and flour. Spoon over the jam in the pastry case.
Arrange the plums, skin-side up, in circles over the almond mixture, starting from the outside, until it is covered. Sprinkle over the flaked almonds.
Place on a preheated baking sheet and bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 40–45 minutes until risen and set.
Warm the remaining conserve or jam in a small saucepan, then brush over the top of the tart while the tart is still warm. Serve the tart warm in slices with a spoonful of double cream.