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1
In the bowl of a food processor, stir together the flour and salt.
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2
Sprinkle the butter over the top and pulse for a few seconds, or just until the butter is slightly broken up into the flour but still in visible pieces.
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3
Evenly sprinkle the water over the flour mixture, then process just until the mixture starts to come together.
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4
If the dough looks too dry, add 1 or 2 additional tablespoons of water.
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5
Dump the dough onto a work surface, press it together, then divide it in half.
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6
Press each half into a disk, then place the disks in a large zipper-top plastic bag.
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7
Refrigerate the dough for at least 30 minutes or as long as 1 day.
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8
In a saucepan over medium heat, poach the chicken in gently simmering water until opaque, about 15 minutes.
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9
Remove with a slotted spoon and place on a cutting board.
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10
Let cool slightly, then shred the meat, discarding the bones and any bits of gristle and fat.
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11
You should have 3 cups of meat.
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12
Set aside.
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13
Heat the oven to 400 degrees F. In a large, wide saucepan, cook the carrots and leeks in 1 tablespoon of the butter and the olive oil with a sprinkle of salt, stirring occasionally, until the carrots are crisp-tender, about 15 minutes.
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14
Scrape into a bowl.
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15
Melt another 1 tablespoon butter then add the mushrooms.
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16
Cook, stirring, until tender, about 10 minutes.
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17
Add to the carrot mixture.
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18
Set aside.
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19
Melt the remaining 5 tablespoons of butter in the saucepan.
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20
Sprinkle the flour over the top and whisk in.
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21
Cook for a few minutes until bubbly.
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22
Slowly add the chicken stock, whisking constantly until smooth.
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23
Whisk in the milk.
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24
Add the reserved chicken, carrots, leeks, mushrooms, and peas and thyme to the sauce.
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25
Stir to combine.
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26
Taste for salt and add more if necessary.
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27
Season with black pepper.
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28
Set aside.
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29
Have ready 4 fairly deep, 1-1/2-cup ramekins or baking dishes.
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30
On a lightly floured work surface, roll out the dough to a large rectangle about 1/8 inch thick.
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31
Cut out 4 circles that are 1/2 to 1 inch larger than the circumference of your ramekins or baking dishes.
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32
You will have leftover dough; press the scraps together and save them for another use in a plastic freezer bag (they can be frozen for up to 3 months).
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33
Divide the filling among the ramekins and top with the pie dough.
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34
Tuck the edges of the pie dough underneath and fit the dough just inside the ramekin.
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35
Place the ramekins on a baking sheet.
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36
Cut a few slashes in each crust for steam to escape during baking.
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37
Brush the egg and water mixture on the dough.
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38
Bake until bubbly and the pastry is brown and cooked through, about 40 minutes.