For the pastry, rub the butter into the flour and salt in a mixing bowl using your fingertips until the mixture resembles breadcrumbs.
Sprinkle in 2-3 tablespoons of cold water and then use a knife to stir the mix together. This can also be done in a food processor.
Knead the mixture gently to form a dough, then wrap the pastry in greaseproof paper and place to chill in the fridge for twenty minutes.
Preheat the oven to 200°C/400°F/gas 6. (gas 6) Roll out the pastry on a lightly floured surface and use to line a 24cm loose-based, fluted tart tin. Prick the base all over with a fork, and then chill in the fridge for 10 minutes. Cover the pastry with a circle of greaseproof paper and scatter a layer of dried or baking beans on top.
Place the tart case on a baking sheet and bake for 10 minutes. Remove from the oven, lift off the beans and paper and then place back in the oven for a further 5 minutes.
In the meantime whip up the filling: Cream the butter and sugar together in a mixing bowl using a wooden spoon.
Beat in the egg yolks, followed by the flour and ground almonds. Slice the pear halves into two parallel slices but don’t separate fully.
Spread the almond mixture over the tart base and using a spatula, place each pear half in the tart tin with the narrow half pointing towards the centre.
Bake the tart for 20-25 minutes until golden and firm. Leave in the tin to cool slightly and then cool completely on a wire rack before serving.