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Roll out the pastry on a lightly floured surface until big enough to line an 18 x 28cm tart tin or a 23cm round tart tin. Carefully lift the pastry into the tin, leaving any extra hanging over the sides. Prick the base of the pastry with a fork, sit the tin on a baking sheet and chill for 30 mins.
Heat oven to 200C/180C fan/gas 6. Line the pastry with baking parchment and fill with baking beans. Put in the oven and bake blind for 15 mins. Remove the beans and paper, and bake for a further 10 mins until the pastry is biscuity. Decrease the oven to 160C/140C fan/gas 3, and trim the pastry edges.
To make the cardamom frangipane, beat all the ingredients together with an electric whisk. Dollop into the tin and spread evenly to fill. Peel, halve and core the pears – scoop out the core with a melon baller, if you have one. Brush with a little lemon juice. Arrange the pears in the tin, pushing them a little into the frangipane. Scatter with a few more flaked almonds and bake for 50 mins until the filling is risen, golden and firm to the touch. Serve warm or cold, drizzled with a little honey.