Preheat the oven to 200C/400F/Gas 6.
Roll out the pastry on a lightly floured work surface and use it to line a 27cm/10¾in loose-bottomed, fluted tin. Line the pastry case with baking parchment or aluminium foil and fill with ceramic baking beans (alternatively use uncooked rice or lentils). Bake blind for 15 minutes, then remove the parchment and baking beans and return the pastry to the oven for an extra eight minutes, or until the pastry looks dry and faintly coloured. Set aside to cool.
Reduce the oven temperature to 180C/350F/Gas 4.
To make the filling, beat the butter and sugar together until light and fluffy. Add the ground almonds, flour and eggs. Mix to thoroughly combine. Stir in the vanilla extract and one tablespoon of flaked almonds.
Spread the apricot jam on the base of the cooled pastry case. Spread the frangipane mixture over the apricot jam. Use a pallet knife to smooth the filling. Sit the pears on the filling and gently press them down. Scatter over the remaining flaked almonds.
Bake for 25-30 minutes, or until the filling is set and golden-brown.
Leave to cool in the tin before serving. Serve with whipped cream.