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For the pastry, put the butter and flour in a food processor and whizz to fine crumbs, then pulse in the sugar. Mix the egg yolks with 2 tsp cold water and, with the blade running, pour in the liquid to bring the pastry together. If it doesn’t come together, add 1-2 tsp more water until it does.
Tip the pastry onto a lightly floured surface and bring together to make a flat disc, then roll out to line a 23cm loose-bottomed tart tin. Leave the pastry overhanging the tin and prick the bottom of the pastry case with a fork. Chill for 30 mins.
Heat oven to 200C/180C fan/gas 6. Line the pastry case with some crumpled baking parchment, fill with baking beans, then blind-bake for 15 mins. Carefully remove the parchment and beans, and bake for a further 10 mins or until the pastry looks golden and biscuity. Remove the case from the oven and trim the edges of the pastry with a sharp knife. Can be done the day before. Lower oven to 180C/160C fan/gas 4.
While the case is baking, make the filling. Cook the cranberries in a shallow pan over a medium heat with 2 tbsp water for 15 mins until pulpy. Push the fruit through a sieve over a bowl; discard the seeds and skins.
Put the cornflour in a clean pan and whisk in the lemon and orange juice until smooth. Add the sugar and cranberry purée, and heat until the mixture has bubbled and thickened, stirring constantly. Remove from the heat, add the butter and beat until melted. Add the egg yolks and whole egg to the pan, beat well and return to a medium heat. Keep stirring vigorously for 5 mins until the mixture thickens and drops off the spoon. Remove from the heat and set aside.
Meanwhile, make the meringue. Put the egg whites in a large clean bowl and whisk to stiff peaks. Add half the sugar, a spoonful at a time, whisking between each addition until stiff again. Whisk in the cornflour and remaining sugar until shiny and thick.
Pour the filling into the pastry case. Put spoonfuls of meringue around the edge of the filling so it just touches the pastry and pile the rest into the centre, spreading so that it covers the filling. Bake for 18-20 mins until the meringue is crisp and slightly coloured. Let the pie sit in the tin for 30 mins, then remove and leave for at least another 30 mins before slicing. Can be made several hours ahead.