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1
In a small bowl, whisk the yeast with the buttermilk until it dissolves.
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2
Let stand for 10 minutes, until foamy.
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3
In the bowl of a stand mixer fitted with the dough hook, mix the bread flour with the sugar and salt.
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4
With the machine at medium speed, add the yeast mixture, then add 4 of the eggs, 1 at a time, beating well after each addition.
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5
Drizzle in the butter and beat for 10 minutes; the dough will look slightly greasy.
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6
Transfer to an oiled bowl, cover with plastic wrap and refrigerate overnight.
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7
Let the dough stand at room temperature for 1 hour before proceeding.
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8
Lightly oil a 10-by-5-inch loaf pan.
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9
On a work surface, roll out the dough to a 10-by-8-inch rectangle.
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10
With a long side facing you, fold the dough in thirds and fit seam side down in the prepared loaf pan.
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11
Cover with plastic wrap and let rise in a warm place until doubled in bulk, about 2 1/2 hours.
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12
Preheat the oven to 425 and set a rack in the center.
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13
In a small bowl, beat the remaining egg.
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14
Brush the top of the brioche with some of the egg wash and make a 1/4-inch-deep slit down the center of the loaf.
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15
Bake for 20 minutes.
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16
Brush the top again with egg wash and bake for 20 minutes longer, until the top is deep golden and an instant-read thermometer inserted in the center of the loaf registers 182.
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17
Transfer the brioche to a rack to cool for 30 minutes, then unmold and let cool completely.
