Grease a 23cm/9in loose-bottomed, deep-sided tart tin with butter and dust with flour.
For the pastry, sift the flour and icing sugar into a bowl, then rub in the butter with your fingertips until the mixture resembles breadcrumbs.
Make a well in the centre of the mixture. Crack in the eggs and stir using your fingertips until the mixture comes together as a sticky dough.
Turn out the dough onto a lightly floured work surface and knead lightly until smooth. Flatten to a thickness of 1cm/½in using the palms of your hands, then cover with cling film and chill in the fridge for at least 30 minutes.
Meanwhile, for the filling, add all of the prunes, 150ml/5fl oz of the Armagnac, 100g/3½oz of the caster sugar, and 100ml/3½fl oz of water to a saucepan. Bring the mixture to the boil, then turn off the heat and set aside for 5-10 minutes, or until the prunes have absorbed the liquid and plumped up and softened.
Roll out the pastry onto a lightly floured surface to a thickness of 3mm.
Carefully line the prepared tart tin with the pastry, pressing it into the edges of the tin. Take care not to stretch or break the pastry.
Blend half of the soaked prunes with 3 tablespoons of the soaking liquid in a food processor until smooth and puréed. Spread this mixture over the base of the pastry case.
Preheat the oven to 190C/170C Fan/Gas 5.
For the filling, beat the butter and the remaining caster sugar until pale and fluffy. Add the eggs and egg yolk, one at a time, beating well after each addition, until they have all been fully incorporated into the mixture. Fold in the flour and ground almonds carefully with the last of the Armagnac.
Spoon the mixture into the pastry case and smooth the top. Decorate the top of the filling with the remaining soaked prunes and the blanched whole almonds (reserve the remaining soaking liquid).
Bake the tart for 25-35 minutes, or until the filling is golden brown, puffed up slightly and darker brown around the edges.
Just before serving, heat the remaining soaking liquid in a small pan. Bring to the boil, then reduce and simmer for 5-10 minutes, or until sticky and syrupy.
When the tart comes out of the oven, trim the excess pastry from the edges to give a clean edge and brush the top with the Armagnac syrup.
Whisk the double cream in a bowl until soft peaks form when the whisk is removed. Gently whisk in the remaining Armagnac. Dust the tart with icing sugar.
Serve the tart hot or warm with the Armagnac cream.