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1
Position an oven rack in the middle of the oven and preheat to 425 degrees F.
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2
For the filling: Place 1 tablespoon vegetable oil into a 10-inch cast-iron skillet and set over high heat until it shimmers.
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3
Add the chicken, season with 1 teaspoon of salt, and cook, stirring occasionally, until the chicken is no longer pink on the outside but not dry, 4 to 6 minutes.
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4
Remove the chicken from the skillet and set aside in a medium bowl.
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5
Decrease the heat to medium and heat the remaining tablespoon vegetable oil in the skillet until it shimmers.
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6
Add the onions, mushrooms, carrots, celery, garlic, remaining 1 1/2 teaspoons of salt, black pepper, dried thyme, and dried tarragon, and stir to combine.
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7
Cook, stirring occasionally, until the onions have softened, about 5 minutes.
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8
Add the butter and melt.
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9
Stir in the flour and cook for 1 to 2 minutes.
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10
Gradually stir in the chicken broth and milk.
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11
Bring to a simmer, stirring continually.
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12
Continue stirring until the sauce thickens, about 3 minutes.
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13
Remove the skillet from the heat and stir in the peas, thyme, tarragon, and reserved chicken.
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14
Cover and set aside.
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15
For the crust: Combine the bread flour, whole wheat flour, and salt in a medium mixing bowl.
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16
Place in the freezer for 1 hour.
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17
Place the flour mixture and butter in a mound on a clean work surface.
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18
Use a bench scraper to cut the butter into the flour until the mixture is crumbly and the butter pieces are about the size of almonds.
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19
Add the ice water, 2 tablespoons at a time, and mix into the dough, using the bench scraper, until it just barely comes together.
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20
Do not add too much water, it will come together.
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21
Shape into a rectangle and pound with a rolling pin until it is about the size of a sheet of notebook paper, approximately 8 1/2 by 11 inches.
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22
Use the bench scraper to fold the dough into thirds, like a letter.
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23
Pound with the rolling pin until the piece of dough is again the size of a sheet of notebook paper and rotate 90 degrees.
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24
Repeat the pounding, folding, and rotating 2 more times for a total of 4 turns of the dough.
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25
Pound with rolling pin and fold the shorter sides of the rectangle in towards the center, from top to bottom, and then fold in half, like a book.
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26
Wrap in parchment paper and refrigerate for 1 hour.
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27
For the egg wash: Combine the beaten egg and water in a small dish and set aside.
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28
To build the pie: Divide the warm filling into 4 (16-ounce) ramekins and place on a half sheet pan lined with parchment paper.
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29
Remove the puff pastry from the refrigerator.
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30
Divide in half.
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31
Return one half to the refrigerator.
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32
Sprinkle lightly with flour and roll to 1/4-inch thick and, using your ramekins as a guide, cut 2 circles that are 1/2 inch wider than the rim, using a sharp knife or pizza cutter.
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33
Repeat with the other half of the dough.
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34
Refrigerate excess dough for another use.
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35
Brush each dough round with egg wash and place egg washed-side down onto the top of each filled ramekin.
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36
Brush the top of the pastry with egg wash. Bake for 15 minutes.
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37
Decrease the heat to 400 degrees F and bake until the crust is puffed and golden brown and the filling is bubbly, another 15 to 20 minutes.
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38
Cool on a rack for 10 minutes before serving.
