Mix flour, salt, and butter for the crust; add water, and form dough. Chill 1 hour.
Season, cook chicken 5-7 min per side; shred, set aside.
Sauté onion, carrots, celery 5-7 min; add garlic 1 min.
Stir in flour, then broth, milk; simmer until thick. Add peas, corn, herbs, and chicken.
Roll out crusts; fill pie dish, top with second crust, crimp, vent. Brush with egg.
Bake at 400°F 35-40 min. Cool 10-15 min; serve with salad.