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1
In a small saucepan, heat 3/4 cup of the milk until warm to the touch but not hot (about 105 degrees F to 115 degrees F on an instant-read thermometer).
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2
Transfer the warm milk to a large bowl and sprinkle the yeast on top.
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3
Set aside for about 15 minutes to activate the yeast.
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4
Sift the flour, sugar, salt, mahlepi (if using), and mastic (if using) together into a large bowl; set aside.
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5
In a small saucepan, melt 7 tablespoons of the butter.
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6
Let the butter cool, then transfer to a medium bowl.
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7
Add the eggs and orange zest and beat together.
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8
Stir the egg mixture into the yeast mixture until combined.
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9
Using a spoon, stir the flour mixture into the yeast-egg mixture until combined.
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10
Turn the dough onto a floured work surface and knead until smooth, flouring your hands and the surface as needed, about 10 minutes.
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11
Coat a baking sheet and a 16-inch piece of plastic wrap with the remaining 1 tablespoon butter.
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12
Set the dough on the baking sheet and cover it with the plastic wrap, butter side down.
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13
Let rise in a warm place until doubled in size, about 2 hours.
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14
Remove the plastic wrap and set it aside.
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15
Divide the dough into 3 equal pieces (about 12 ounces each).
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16
Roll the pieces into 1-1/4-by-16-1/2-inch ropes.
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17
Pinch all 3 pieces together on one end to secure, then braid the ropes, entwining the red hard-boiled egg (if using) into the bread.
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18
Pinch the other end of the ropes together to secure the braid.
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19
Set the braided dough on the prepared baking sheet, cover with the buttered plastic wrap (butter side down), and let rise in a warm place until doubled in size, about 1 hour.
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20
Meanwhile, heat the oven to 350 degrees F and arrange a rack in the middle.
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21
In a small bowl, beat together the egg yolk and remaining 1 tablespoon milk.
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22
With a pastry brush, evenly brush the egg mixture over the risen dough, then sprinkle the almonds over top, pressing the nuts gently into the dough.
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23
Bake until the bread is browned and the internal temperature reaches 190 degrees F on an instant-read thermometer, about 30 minutes.
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24
Let cool before serving.