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1
Place milk in a small bowl, add yeast, and stir to combine; let sit 5 minutes.
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2
Place sugar and 4 cups of the flour in the bowl of a stand mixer fitted with a hook attachment and mix on low speed to combine.
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3
Pour in milk-yeast mixture and mix until all of the flour is moistened, about 2 minutes.
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4
Add salt, then eggs one at a time, waiting until each egg is completely incorporated before adding another.
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5
Continue mixing until all the eggs are completely incorporated.
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6
Increase the speed to medium and continue to mix until a smooth and elastic dough forms, about 10 minutes.
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7
Increase the speed to medium high and add the butter, one piece at a time, waiting until each piece is incorporated before adding another.
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8
Continue mixing until the dough looks smooth and shiny but is not sticky and doesnt tear when lightly stretched, about 8 to 10 minutes total.
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9
If it is too sticky, add some of the remaining 1/2 cup flour, little by little, just until its no longer sticky.
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10
(Avoid the temptation to add too much flour.)
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11
Lightly oil a large bowl and place the dough inside.
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12
Cover with a slightly damp towel or plastic wrap and let sit in a warm place (about 70 degrees F) until the dough has increased in size by a third, about 80 to 90 minutes.
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13
Pull the outer edges of the dough into the center to form a ball, and rotate so the seam is on the bottom.
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14
Cover with plastic wrap and refrigerate overnight (chilling slows the fermentation process and makes the dough easier to shape).
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15
Set the dough at room temperature.
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16
Remove the plastic wrap and cover the bowl with a damp towel.
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17
Let the dough come to room temperature, about 3 to 4 hours.
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18
Meanwhile, prepare the topping.
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19
Place flour, powdered sugar, baking powder, and salt in a large bowl and whisk to combine; set aside.
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20
Place butter in the bowl of a stand mixer fitted with a paddle attachment and beat on medium-high speed until light in color and fluffy, about 3 minutes.
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21
Stop the mixer to scrape down the sides and bottom of the bowl with a rubber spatula.
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22
With the mixer on low speed, add the flour mixture and vanilla or cinnamon, mixing until the ingredients are combined and a handful forms a ball when squeezed together, about 2 minutes.
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23
Line 3 baking sheets with parchment paper; set aside.
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24
Divide the dough into 24 equal pieces.
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25
Roll the pieces into smooth balls by cupping your hand around the dough, pressing down very lightly, and rolling it against the work surface.
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26
(If it starts to stick and smudge the surface, dust the surface very lightly with flour.)
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27
Place 8 dough rounds on each baking sheet about 2 inches apart; set aside.
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28
Divide the topping into 24 portions.
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29
Roll a portion of topping in your hands, place it on a work surface, and flatten it with a flat spatula or your hands until its about 2 1/2 to 3 inches in diameter.
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30
Using a spatula, remove the flattened topping from the work surface and drape it over a dough round.
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31
Repeat with the remaining topping and rounds.
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32
Score the topping with the tip of a sharp paring knife to make parallel curved lines resembling a seashell.
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33
Let the dough rounds sit at room temperature until increased in size by a third and the dough springs back when pressed lightly on the side, about 45 to 60 minutes.
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34
Meanwhile, heat the oven to 350 degrees F and arrange racks in the upper and lower thirds.
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35
Bake 2 sheets of the conchas, rotating bottom to top rack and back to front halfway through the baking time, until the bottoms and sides are golden, about 30 to 40 minutes.
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36
For the remaining sheet of conchas, arrange a rack in the middle and bake 25 to 30 minutes, rotating the sheet back to front halfway through the baking time.
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37
Allow the buns to cool, or eat warm.