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Preheat the oven to 200°C.
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In a large bowl, combine the vanilla, lemon zest, caster sugar, flour and salt.
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Add the figs and blackberries and toss very gently to coat.
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On a piece of baking paper, roll out the rye pastry into a large circle, about 30cm in diameter.
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Spread the hazelnut frangipane over the middle circle, leaving a 4-5cm border around the edge.
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Arrange the fruit gently on top of the frangipane. Fold the edges of the pastry over the fruit and press to seal any folds. Seal any cracks in the rye pastry. Chill the tart in the fridge for 15 minutes.
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Whisk together the egg with a teaspoon of water and a pinch of salt to form an egg wash. Brush over the pastry edge of the tart, then sprinkle with demerara sugar.
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Bake for 30-40 minutes until the pastry is golden brown and the fruit is bubbling. Let cool about 15-20 minutes before serving with mascarpone or ice cream.