Roll out the pastry nice and thin to line a 20cm fluted loose-based flan tin. Prick the base and return to the fridge to stay cool.
Make the filling: Whisk the eggs and sugar with electric beaters until pale and light. Fold in the ground almonds then the butter and finally the flour and baking powder.
Assemble the tart: Put some of the almond mixture into the pastry case then sit the peeled, halved pears on top. Fill in the gaps with the remaining almond mixture. The pears will end up with a thin covering of almond mix. This is good as it prevents them drying out in baking.
Bake the tart in a pre-heated oven at 180 C / Gas 4 for about 40 minutes. Serve warm (not hot).