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Preheat the oven to fan 180C/ conventional 200C/gas 6. Roll out pastry on a lightly floured surface and use to line a shallow loose-bottomed 25cm flan tin. Make sure the pastry comes above the rim – it may shrink in baking and the filling could spill. Chill for 30 minutes.
Meanwhile, cut the figs in half lengthways and sit them cut side up on a roasting tray. Mix the orange juice and honey in a bowl, pour over the figs and roast for 10-12 minutes until just soft. Drain off any juice into a saucepan and reserve.
Prick the base of the chilled pastry case all over with a fork, then line with greaseproof paper and fill with baking beans. Bake blind for 15 minutes. Remove the paper and beans and bake for a further 5-10 minutes until the pastry is golden. Remove from the oven and reduce the temperature to fan 130C/conventional 150C/ gas 2. Leave the pastry case to cool slightly before filling.
Cream butter and sugar in a food processor or with an electric beater until smooth and pale. Tip in the ground almonds and zest and whizz briefly to combine. Add egg yolks and 1 tbsp of the reserved fig juice and whizz again until smooth. Spread evenly over the pastry case.
Gently press the figs cut side up into the almond mixture. Bake for 11⁄4 hours or until it’s golden all over (don’t worry if the centre still seems soft – a little gooeyness is good). Leave in the tin for 15 minutes, then remove sides and transfer on its base to a wire rack to cool.
Before serving, take the tart off its base and transfer to a flat platter or board. If you have juice left from roasting the figs, bring it to the boil and simmer for 1-2 minutes until sticky and syrupy. Brush this over the figs and serve as soon as possible, while the syrup is still glossy on the figs (it will start to seep through into the filling if you leave it too long).