First, make the pastry. Sieve the flour, ground almonds and a pinch of salt into a large bowl. Add the butter and lightly rub in until you have no large lumps. Make a well in the centre, mix the egg yolk and sugar together until the sugar is dissolved, then pour into the well. Stir until the liquid is well combined and you have a smooth, very soft pastry. Wrap in baking parchment and rest in the fridge for 1 hr.
Roll the pastry between two sheets of baking parchment, then line a deep 23cm fluted tart tin with the pastry – you will need to work quite quickly when it comes up to room temperature. Don’t worry if it tears or breaks, just patch it up – it will knit together again when it bakes. Return the pastry case to the fridge while you make the filling. Heat oven to 180C/160C fan/gas 4.
To make the frangipane, beat together the sugar and butter until fluffy, then add the egg, egg yolk and ground nuts. Fill the tart case with the frangipane and top with the apricots. Press them into the frangipane and sprinkle with the chopped pistachios. Bake in the oven for 40-50 mins until the pastry is crisp and golden and the frangipane is puffed and coloured.