Preheat oven to 375°. Melt butter in a large skillet over medium heat; add leeks, and sauté 3 minutes. Sprinkle with flour; cook, stirring constantly, 3 minutes. Whisk in chicken broth; bring to a boil, whisking constantly. Remove from heat; stir in chicken and next 5 ingredients.
Roll each pastry sheet into a 12- x 10-inch rectangle on a lightly floured surface. Fit 1 sheet into a 9-inch deep-dish pie plate; spoon chicken mixture into pastry. Place remaining pastry sheet over filling in opposite direction of bottom sheet; fold edges under, and press with tines of a fork, sealing to bottom crust. Whisk together egg and 1 Tbsp. water, and brush over top of pie.
Bake at 375° on lower oven rack 55 to 60 minutes or until browned. Let stand 15 minutes.