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1
Place eggs, wine, and vinegar in a medium, nonreactive bowl and whisk to break up the yolks; set aside.
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2
Place flour, sugar, and salt in a large bowl and whisk briefly to combine.
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3
Add butter and, using a pastry blender or your fingers, blend until pea-size pieces of butter remain, about 2 minutes.
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4
Drizzle egg mixture over flour mixture and combine with a wooden spoon or rubber spatula until all flour from the bottom of the bowl is incorporated but the dough has not formed a solid ball, about 2 minutes.
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5
Turn dough out onto a floured work surface and form into 2 round disks.
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6
Wrap each disk in plastic wrap and refrigerate until firm, at least 1 hour.
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7
Meanwhile, pat chicken dry with paper towels and season generously with salt and pepper.
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8
In a large frying pan with a tightfitting lid, melt butter over medium-high heat until foaming.
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9
Place chicken skin side down in the pan and cook until golden brown, about 5 minutes.
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10
Flip and cook the second side until golden brown, about 4 minutes more.
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11
Transfer to a plate and set aside.
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12
Remove all but 3 tablespoons of fat from the pan.
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13
Reduce heat to medium and add onion, bell pepper, oregano, cumin, red pepper flakes, salt, and pepper.
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14
Cook, stirring occasionally, until onion has softened, about 4 minutes.
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15
Add tomatoes and wine, stir to combine, and bring to a simmer.
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16
Place reserved chicken and any accumulated juices back in the pan, cover, and reduce heat to low.
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17
Simmer until chicken is no longer pink, about 25 minutes.
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18
Transfer chicken to a cutting board.
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19
(If there is still liquid in the pan, increase the heat to medium and continue cooking the mixture, uncovered, until the liquid has evaporated.)
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20
Remove the pan from heat and set aside.
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21
When the chicken is cool enough to handle, remove the meat and discard the skin and bones.
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22
Finely chop the meat and return it to the pan.
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23
Add olives, cilantro, and vinegar, season with more salt and pepper as desired, and stir to combine.
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24
Transfer mixture to a medium bowl and refrigerate uncovered until cold, at least 30 minutes.
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25
Heat the oven to 375 degrees F and arrange a rack in the middle.
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26
Line 2 baking sheets with parchment paper; set aside.
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27
Combine egg and water in a small bowl and beat together; set aside.
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28
Remove a dough disk from the refrigerator and place it on a lightly floured work surface.
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29
Sprinkle the top with flour and roll the dough to 1/16-inch thickness, flouring as needed to prevent sticking.
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30
Using a 4-1/2-inch round cutter, stamp out as many rounds as possible (you should have 4 or 5).
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31
Gather the dough scraps, rewrap in plastic, and refrigerate.
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32
Roll and stamp the second dough disk, gathering the scraps, wrapping them in plastic, and refrigerating.
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33
Place 2 level tablespoons of the filling in the center of a dough round.
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34
Dip your finger in the egg wash and trace around the edge of the round to moisten.
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35
Place the empanada in your hand and fold the sides up like a taco.
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36
Squeeze the bottom left and right sides together at the edges, and then continue squeezing toward the middle until the entire empanada is sealed.
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37
Lay the empanada flat, press the back of a fork along the rounded edge to further seal and create a pattern, and place on one of the prepared baking sheets.
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38
Repeat with the remaining dough rounds, spacing 10 empanadas at least 1 inch apart on the baking sheet.
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39
Brush the tops with egg wash and bake until golden brown, about 25 to 30 minutes.
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40
Meanwhile, remove the dough scraps from the refrigerator and repeat rolling (only reroll the scraps one time), stamping, filling, and brushing until all of the filling is gone and you have about 10 more empanadas on the second baking sheet.
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41
Remove the first batch from the oven before baking the second batch.
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42
Serve warm or at room temperature.
