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1
Make the brioche dough the day before you want to bake: Place the flour, yeast, sugar, salt, eggs, and milk in a mixing bowl or a stand mixer, mix until it all comes together, then knead for five minutes or so until smooth and slightly elastic. The dough is quite sticky so if you are kneading by hand be prepared to get messy!
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2
Add the butter in lumps and work it into the dough. Again, this is more easily done with a stand mixer but is perfectly possible by hand; just get in there and scrape, squeeze, and knead the dough energetically until the butter is all evenly incorporated and the dough is smooth, soft, and elastic (it will still be quite sticky though).
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3
Place the dough in a bowl with enough room for it to grow, cover, and refrigerate overnight.
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4
Poach the pears the day before baking. To poach the pears, peel, halve and core the pears. Place the water, sugar, cinnamon stick, star anise, cloves, and allspice berries in a small saucepan and heat gently, stirring, until the sugar has dissolved. Add the pears and cover with a round of greaseproof paper that sits on the surface of the liquid and has a hole cut in the center. Bring up to a gentle simmer and cook until tender, about 15 to 20 minutes. The pears should fall off a fork if you stab one. Once tender, remove from the heat and leave to cool; place the pears in their poaching liquid in a covered container and refrigerate overnight.
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5
The following day, remove the dough from the fridge and divide into 4 equal pieces (about 65 grams each). Shape each piece into a ball then roll out on a lightly floured surface into an approximately 5-inch round. Place the discs on a baking tray lined with parchment or a silicone liner, cover loosely with plastic wrap, and set aside to rise for 1 1/2 to 2 hours until puffy and the dough springs back when gently pressed with a finger. They will still be quite thin.
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6
While the dough is rising, make the frangipane. Cream together the butter and sugar until fluffy, in a small bowl beat the egg and add just over half of it to the butter mixture, reserving the rest for the egg wash; add the flour, ground almonds, and almond extract to the butter mixture. Crack open the cardamom pods and grind the seeds in a pestle and mortar and add to the mix. Beat everything together until smooth.
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7
Drain the pears and pat dry, then cut each pear half into thin slices, leaving them attached at the top. Preheat the oven to 400u00b0 F (200u00b0 C).
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8
When the discs have risen, press down the centre of each one with your fingers, leaving a 2-centimeter border around the edge. Spread a scant teaspoon of jam into the depression of each one. Spread about a heaped tablespoon of the frangipane on top of the jam on each tart. Spread the sliced pear halves out into fan shapes and place one on each tart.
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9
Brush the exposed dough with the remaining beaten egg then place the tray in the centre of the oven and bake for about 15 minutes (check after 10) until a deep golden brown, puffed up and cooked through. Gently warm the apricot jam with a splash of water until runny, transfer the tarts to a wire rack and brush all over with the apricot jam to glaze.
