Whisk egg and sugar in a small bowl set over ice-cold water until the sugar dissolves.
Mix in flour until breadcrumbs form, then cut in butter cubes and knead on a floured surface.
Flatten the pastry into a disc, wrap in film, and chill in the fridge for 30 minutes.
Process pistachios and almonds into a paste, then beat with butter, sugar, eggs, and honey.
Whisk sugar, yolks, and cornflour, then gradually add boiled milk, honey, and cardamom pod.
Thicken the mixture over heat, stir in butter, and chill in the fridge covered with film.
Preheat the oven to 190°C and heat a baking sheet on the top shelf.
Roll pastry to 2-3mm thickness and line a 23cm tart tin before freezing for 15 minutes.
Blind bake the tart shell with weights for 7 minutes, then without for another 7 minutes.
Brush the base with egg white, bake for 2 minutes, and allow to cool completely.
Spread frangipane in the case and bake for 15-20 minutes with foil protecting the edges.
Pipe on the crème pâtissière, arrange fruit, and brush with warmed apricot jam glaze.
Top the tart with crushed pistachios and flaked almonds before serving.