For the pastry case, add a little ice-cold water to a large mixing bowl. Place a smaller metal bowl on top, and place the egg and sugar into the smaller bowl. Whisk the egg and sugar together until the sugar has dissolved.
Add the flour and combine until the mixture resembles breadcrumbs. Add the cubes of cold butter, and using a butter knife, cut into the floury mixture. When the mixture begins to come together, turn out onto a lightly-floured worktop and knead quickly for a few seconds. Cover the pastry with cling film, flatten into a disc and put in the fridge for about 30 minutes.
For the pistachio frangipane, blend the pistachios and almonds to a paste in a food processor. In a bowl beat the butter and sugar together then add the eggs and honey. Continue to beat a little, then add the nuts and mix until completely combined.
For the crème pâtissière, combine the sugar, egg yolks and cornflour in a mixing bowl. Place a small saucepan over a high heat bring the milk, honey and cardamom pod to the boil. Slowly pour the boiled milk onto the egg yolks, whisking constantly. When combined return the mixture to the pan. Over a medium heat whisk the crème pâtissière until very thick. Remove from the heat and mix in the butter. Cover with cling film and chill in the fridge.
Preheat the oven to 190C/375F/Gas 5. Put a baking sheet on the top shelf to heat up.
Remove the pastry from the fridge, unwrap it and sandwich it between two large pieces of cling film. Roll out the pastry until it is 2-3mm/1/8in thick and place into a 23cm/9in tart tin (the best way is to keep the rolled out pastry attached to the cling film on one side, flip it over, cling film side up, and lay the pastry into the tin). Press down into the grooves of the tin, remove the cling film and leave the surplus hanging over the sides. Chill the pastry case in the freezer for 15 minutes.
Cut a piece of baking paper large enough to cover the tart case. Scrunch it up slightly, sit it in the pastry tin and fill with baking beans. Bake in the oven for seven minutes. Remove the baking paper and beans then bake for a further seven minutes.
Brush the bottom of the pastry case with egg white and bake for a final two minutes. Set aside until completely cooled.
Spread the frangipane onto the base of the pastry case, and cover the pastry edges with doubled foil so they don’t burn when cooking again. Bake in the oven for 15-20 minutes, or until the frangipane is cooked and lightly browned. Remove the foil and set aside to cool.
For the topping, pipe on the crème pâtissière and arrange the fruit on top in concentric circles. Make a glaze by heating the apricot jam with one tablespoon of water in a small saucepan. Sieve to remove any lumps. Then gently brush the glaze over the fruit. Finish by sprinkling over the pistachios and flaked almonds.