To make the pastry, put the flour, icing sugar and salt in a food processor and blitz briefly to combine. Add the butter and blitz until the mixture resembles breadcrumbs. (Or you can rub the butter into the flour/icing sugar in a bowl, using your fingertips.) Add the egg yolk and enough milk to bring the dough together in large clumps. Tip on to a lightly floured surface and knead lightly into a ball. Wrap in cling film and chill for 30 minutes.
Preheat the oven to 200°C/Gas 6 and grease a large baking tray or line with baking parchment.
Peel, quarter and core the pears, then slice each quarter lengthways in two. Heat the butter and brown sugar together in a frying pan over a medium heat and, when bubbling, add the pears. Cook gently for a few minutes, until the pears are just tender and bubbling in a toffeeish sauce. Drain the pears in a sieve over a bowl, retaining all the sauce. Allow to cool. Set the sauce aside.
For the frangipane mixture, cream the butter and sugar together in a bowl until fluffy. Add the egg, flour, ground almonds and vanilla and beat well until evenly combined.
Roll out the pastry into a rough rectangle, no thinner than 4mm, and trim to about 30 x 25cm. Place on the prepared baking tray. Spread the frangipane mixture over the pastry, leaving a slight border around the edge. Arrange the cooked pears over the frangipane, then sprinkle with the demerara sugar and flaked almonds. Bake for 20 minutes until the pastry is golden brown at the edges.
Allow the tart to cool for 10 minutes or so before serving. Meanwhile, warm the toffee sauce through, stirring well to re-emulsify if it has separated slightly.
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