Preheat the oven to 210°C/fan 190°C/gas mark 7. Pulse together the flour and butter in a food processor until it resembles breadcrumbs. Add the sugar and egg yolks and pulse again until it comes together. Transfer to a bowl and lightly knead until smooth and evenly coloured. Shape into a disc and wrap with clingfilm, then place in the fridge to chill for around 30 minutes, until firm but still slightly pliable.
To make the filling, mix the eggs with the sugar, then add the lemon juice, zest and double cream. Cover and place in the fridge while you cook the pastry.
Preheat the oven to 190°C/fan 170°C/gas mark 5. Roll out the pastry to ½cm thick, then transfer it to a 22cm-tart tin and press to line the tin well, making sure it is evenly thick all around. Cut off the excess pieces around the edge. Place in the fridge to firm up for 15 minutes.
Blind bake the pastry for 15 minutes, lined with greaseproof paper and baking beans. Once the edges feel firm, remove the baking beans and greaseproof paper then brush the inside with egg white to create a seal and prevent any leakage when you add the filling. Return to the oven and bake for a further 5-8 minutes until golden, then leave to cool.
Lower the oven to 150°C/fan 130°C/gas mark 2. Once the pastry has completely cooled, transfer the filling mixture to a jug and carefully pour it into the pastry. Carefully transfer to the oven and bake for 40-45 minutes until just set (it should still have a very slight wobble as it will firm up as it cools). Leave to cool before serving.