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1
To make the brioche: Put the yeast and water in the bowl of a stand mixer and stir gently to combine. Let it sit until it bubbles, about 5 minutes.
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2
Add the flour and salt, then use the dough hook to stir the flour into the yeast mixture on low speed. Stop the mixer a few times and use a spatula to scrape the sides of the bowl. The dough will be very shaggy and dry.
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3
Add the eggs. Mix gently to combine, then add the sugar. Turn the mixer up to medium-low and mix until the dough forms a ball, about 4 minutes.
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4
Turn the mixer back down to low and mix the butter into the dough in 2-tablespoon chunks, beating until each piece is almost completely incorporated before adding the next piece. Make sure to take this step nice and slowly to ensure that the dough is evenly mixed and kneaded. Stop periodically to pull the dough from the hook and scrape the sides of the bowl to ensure even mixing. The dough will be very soft and billowy.
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5
Once all of the butter has been incorporated, continue to knead the dough until it pulls away from the sides of the bowl, about 10 minutes
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6
Transfer the dough to a clean bowl and let it rise at room temperature until it has doubled in size, 40 to 60 minutes. Knead the dough in the bowl a few times to release the air, then cover and transfer the bowl to the refrigerator. Check on the dough every half hour or so and gently knead it in the bowl a few times until it is chilled and stops rising, about 2 hours. Let the dough rest at least overnight and up to 24 hours in the refrigerator.
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7
For the Filling: Peel, core, and slice the apples and pears into 1/4-inch slices. Put the sliced fruit in a large bowl and toss gently with the lemon juice. Add the sugar, cinnamon, vanilla bean seeds, and a pinch of salt. Toss gently to combine.
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8
Melt the butter in a large skillet over medium heat. Add the fruit and saute gently until the fruit has softened slightly and the fruit juices have thickened, 7 to 10 minutes. Remove the fruit to a bowl to cool.
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9
When the fruit has cooled, add the flour and stir gently to combine.
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10
If your brioche dough has been in the refrigerator, take it out about 15 minutes before rolling to let it warm up a bit. Then, on a piece of lightly floured parchment paper, roll the brioche dough out into a roughly 10 x 15-inch rectangle about 1/3-inch thick. Don't worry too much if the rectangle isn't perfect. Move the parchment paper and dough to a baking sheet to finish assembly.
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11
Pour the apple mixture down the center of the dough. Use a pastry wheel or kitchen scissors to cut the dough surrounding the filling into diagonal strips about 1 1/2-inch wide. Make sure to leave a border of uncut dough around the filling.
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12
Fold the dough strips over the filling, alternating sides so the dough looks braided. Brush any loose flour from the parchment paper and the surface of the dough. Cover loosely with plastic wrap and let rise until puffy and almost doubled in size, about 40 minutes. While the dough is rising, prepare the streusel.
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13
In a small bowl stir the flour, sugar, cinnamon and salt together. Add the butter and mix it in with your fingers until crumbs form.
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14
When you are ready to bake preheat the oven to 350u00b0 F. Whisk the egg and gently brush it over the dough. Scatter the streusel over the top evenly -- you many have to break it up with your fingers a bit. Slide the baking sheet into the oven and bake until golden brown and cooked through, 30 to 40 minutes. Let the bread cool slightly, then dig in.
