To make the pastry: mix the flour and butter together to resemble breadcrumbs, add the egg and combine. Wrap in cling film and chill for 30 minutes.
Roll out the pastry onto a floured surface and use to line a 22cm x 5cm deep fluted loose bottom tin. Leave the edges of the pastry hanging over the edges of the tin.
Beat together the butter, sugar, almonds, Armagnac and eggs. Place the sliced figs into the bottom of the tart case and spoon the frangipan mix on top. Smooth over, then place the quartered figs on top. Bake for 40 minutes.
Meanwhile make the glaze: place the caster sugar, water and Armagnac into a pan and bring to the boil. Allow to bubble for 3 to 4 minutes.
Mix the cream, vanilla bean paste and Armagnac together until thoroughly combined.
To serve: cut the overhanging pastry edges off the tart, remove from the tart case then glaze. Cut into 8 slices and serve each slice with a spoonful of the cream.