Chicken, leek & tarragon pie

Chicken thighs	3 pounds
Carrot, chopped	1
Celery, chopped	2 ribs
Onions, finely chopped	1 + 1
Tarragon springs	3 + 1
Salt	¼ teaspoon +
Pepper, freshly ground
Flour	1 ¾ cups + 2 tablespoons
Butter, unsalted, cold, cubed	13 tablespoon + 1 tablespoon
Eggs, beaten	1 + 1
Lemon, juice plus zest	1 teaspoon
Water, chilled	2 tablespoons
Olive oil	1 tablespoon
Leeks, thinly sliced	2
Sherry	2/3 cup
Cream, light	2/3 cup

1. In a Dutch oven, combine the chicken, carrot, one onion, and three tarragon sprigs. 
2. Season with salt and pepper, and add enough water to cover. 
3. Bring to a boil, and then simmer for 45 minutes. 
4. Remove the chicken; set aside. 
5. Simmer the stock for 30 minutes longer, until reduced in half. 
6. Meanwhile, sift together the flour and salt, and then add 7 tablespoons butter. 
7. Gently and swiftly rub the butter into the flour until it resembles a coarse meal. 
8. Add 6 tablespoons butter, and mix until the size of peas; make a well. 
9. Combine 1 egg, lemon juice, and water. 
10. Gradually pour into the well, using a knife to mix.
    (Not all of the liquid is required, depending on the day and the flour.) 
11. Turn out on a floured surface, and knead until smooth. 
12. Shape into a ball, wrap with plastic wrap, and refrigerate for at least 30 minutes before rolling. 
13. In a large skillet over medium heat, melt 1 tablespoon butter with the oil. 
14. Add the leeks and remaining onion, and gently cook until softened, about 5 minutes. 
15. Increase the heat to high, add the sherry, and simmer rapidly for 3 to 4 minutes, until reduced by half. 
16. Stir in the flour, and mix well for 1 minute. 
17. Pour in the cream, 2/3 cup of the stock (store the remainder for another use), and the lemon zest. 
18. Season with salt and pepper. 
19. Shred the chicken into small pieces, and add to the leek mixture with the remaining tarragon sprig. 
20. Preheat to 350°F with a baking sheet inside. 
21. Using 2/3 of the pastry, line a 12-by-8 dish, and then fill with the chicken mixture. 
22. Brush the edges of the pastry with egg. 
23. Roll out the remaining pastry to create a lid; crimp the edges together to seal. 
24. Trim away any excess, and brush with egg to glaze. 
25. Place on the baking sheet, and bake for 30 to 35 minutes, until golden and crisp. 

Recipe adapted from Pie by Angela Boggiano