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1
To make the crust, combine flour, butter, shortening, salt and sugar in a food processor.
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2
Pulse together just until the mixture is crumbly and butter is broken into small pieces.
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3
Pour 1/3 cup ice water into the machine, and pulse 3 or 4 times.
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4
Squeeze a little dough in your hand to see whether it clumps together and is evenly moist.
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5
If not, add another tablespoon of water, and pulse 1 or 2 times more.
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6
Don't overmix so that the dough forms a ball.
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7
Turn out dough on a large sheet of plastic wrap.
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8
Lift ends of plastic to gather dough together inside.
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9
Press into a large disk, and wrap tightly in plastic wrap.
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10
Refrigerate until ready to use, up to 2 days.
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11
To make the filling, melt 2 tablespoons butter in a large skillet over medium-high heat.
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12
Add carrot, celery, leeks and tarragon, and cook, stirring, just until slightly softened but not browned (reduce the heat if necessary to prevent browning), about 3 minutes.
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13
Transfer cooked vegetables to a bowl, wipe out the skillet, and place it back on the stove.
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14
Add remaining 3 tablespoons butter, and melt over medium heat.
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15
Whisk in flour, and cook, whisking, until the mixture bubbles and smells cooked.
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16
Do not let it brown.
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17
Whisk in 2 cups broth, and cook, whisking, 1 minute.
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18
Whisk in cream, and cook 2 or 3 minutes, just until thickened.
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19
Season to taste with salt and pepper.
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20
If the sauce is too thick, whisk in remaining broth.
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21
Heat the oven to 400 degrees.
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22
Add cooked vegetables and peas, chicken and sauce to 8-ounce deep pie dish or other baking dish, mix gently, and taste for seasoning.
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23
Flour a work surface.
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24
Remove dough from refrigerator, and cut in half.
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25
(Set aside half for another recipe.)
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26
Roll out remaining dough, turning and flouring often, and cut a shape approximately the size of your baking dish plus 1 1/2 inches overlap all around.
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27
Whisk egg in a small bowl.
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28
Brush onto rim of dish.
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29
Roll dough up onto the rolling pin, and unroll over dish, so it rests evenly on top of filling.
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30
Press overlap onto the rim and against the outside of the dish, sealing tightly.
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31
Poke tip of knife through crust to create 3 vent holes near the center.
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32
Place on cookie sheet, and place in oven.
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33
Bake 20 minutes, then reduce temperature to 375 degrees.
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34
Bake 15 to 20 minutes more, until crust is golden and filling is bubbling through vents.
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35
Let rest 10 minutes before serving.
