In a large mixing bowl, rub together the first five pastry ingredients until they resemble breadcrumbs. Crack the egg, save the egg white for the filling, and stir in the egg yolk and water and bring together to form a soft dough. Wrap this in cling film, then chill in the fridge for 1 hour.
Preheat the oven to 190°C/ Fan 170°C/ Gas 5. Roll out the pastry on a lightly floured surface until it is 5mm thick and press this into a 25cm tart tin. Remember to leave an overhanging collar of pastry around the edge as the pastry will shrink in the oven. Line the pastry case with greaseproof paper and ceramic beans, then bake for 15 minutes. Remove the ceramic beans and bake for another 5 minutes.
While the pastry is baking, soak the prunes in 200ml boiling water. Remove the pastry case from the oven and while still warm trim the excess pastry around the edge.
Lower the oven temperature to 170°C/ Fan 150°C/Gas 3.
In a mixing bowl, cream together the butter and sugar then beat in 1 egg. Mix in the ground almonds, flour, baking powder, almond extract, then beat in the final egg and egg white. Stir through the sweet potato.
Drain the soaked prunes (retaining the soaking liquid) and blitz half with the chia seeds and the rum using a hand blender until smooth. Spread this over the base of the pastry case. Chop up the remaining prunes and stir through the almond mixture before spooning this into the pastry shell and smooth out. Bake for 40–45 minutes until the frangipane is just firm to touch.
Finally, mix together the icing (confectioners’) sugar, the almond extract and just enough water to make a thick icing. Pipe this over the tart in whichever design you like once it is cool, then sprinkle with the almonds.