Roll out the pastry to a thickness of about 5mm/¼in. Line a 25cm/10in tart tin with the pastry and bake blind.
Meanwhile, peel and core the apples, slicing the dissolving cookers and chopping the hard eaters into neat 1cm/½in dice. Put both kinds together into a saucepan with the lemon juice and 110g/4oz of the sugar. Heat very gently until the juices begin to run. Cook the fruit, stirring occasionally at a very gentle simmer for 10-15 minutes, until you have a juicy compote of purée Bramleys (or similar) with tender pieces of Cox (or similar).
To make the crumble: preheat the oven to 200C/400F/Gas 6.
Sift the flour into a bowl and rub in the butter until you have fine crumbs, then toss with the hazelnuts and sugar.
Spread the fruit into the cooked pastry case and sprinkle over the crumble in an even layer. Bake in a preheated fairly hot oven for about 30 minutes, until the crumble top is nicely browned.
Serve the pie warm with vanilla ice cream or cream.