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To make the starter: Weigh your flour for the starter; or measure it by gently spooning it into a cup, then sweeping off any excess. Add the yeast and water in a medium-large mixing bowl, cover the bowl, and let the starter rest for 1 hour, until it's bubbly.
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To make the dough: Weigh or measure your flour for the dough, then add it along with the rest of the dough ingredients to the starter. Mix and knead the dough — using your hands, a stand mixer, or your bread machine set on the dough cycle — to form a sticky, elastic dough. Resist the urge to add more flour; it won't clean the sides of the bowl as dough for a traditional sandwich bread (or even brioche dough) will.
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Let the dough rise, covered, in the mixing bowl (or in another bowl, if desired) for 60 to 90 minutes, or until it's doubled in size; it may be a bit slow, so allow it plenty of time.
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To make the topping: Mix together the sugar, salt, vanilla, and softened butter until smooth. Stir in the flour in two additions, mixing to make a thick paste. (Note: You'll use the egg white later.) Cover the bowl and set the topping aside.
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Transfer the dough to a greased or floured work surface, and divide it into 10 pieces (about 89g each). Roll each into a ball.
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Place the balls of dough onto a greased or parchment-lined baking sheet, leaving some space between them.
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To finish the conchas: If coloring the conchas, divide the topping into the number of colors you'd like to make (it's easiest to do either 2 or 5; see "tips," below for details). Incorporate food coloring until you reach the desired hues. Divide the topping into 10 total portions (about 24g each). Flatten each portion into a 3" to 4" disk by placing portions between two pieces of parchment or wax paper, and rolling with a rolling pin or flattening with your fingers.
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Lightly beat the egg white. Brush the top of each shaped concha with some of the beaten egg white, then add one of the disks of topping. Flatten the rolls slightly.
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Let the conchas rise for 30 to 45 minutes, covered, until they're noticeably puffy.
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While the conchas are rising, preheat your oven to 350°F with a rack in the center.
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Just before baking, use a sharp knife or lame to cut designs into the topping; don't cut into the dough below.
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If you have a second baking sheet, nest the pan of conchas into it; this extra layer of protection will help prevent the conchas' bottoms from over-browning as they bake.
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Bake the conchas for 18 to 24 minutes, until they're golden brown. Remove them from the oven and let them rest on the pan until they're cool enough to handle. Enjoy conchas warm or at room temperature.
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Store any leftover conchas, well wrapped, for three days at room temperature; freeze for up to a month.