Preheat oven to 375°. Heat oil in large saucepan over medium-high heat. Add chicken and cook 5 to 7 minutes or until no longer pink, stirring occasionally. Remove chicken from pan and transfer to large bowl.
Add celery, carrots, potato, onion and salt to pan; cook 5 minutes, stirring frequently. Add wine, scraping any browned bits off bottom of pan. Simmer 12 to 15 minutes or until potato is almost tender, stirring frequently (adding more wine as needed so there is some liquid in the pan at all times). Add garlic, snap peas and rosemary; cook 2 minutes. Transfer vegetables to bowl with chicken.
Lower heat to medium; melt butter in pan. Whisk in flour and cook 2 minutes, stirring constantly. Slowly whisk in chicken stock. Bring to a boil and cook 4 to 6 minutes or until slightly thickened (sauce will continue to thicken in oven); stir in milk, lemon juice and black pepper. Remove from heat; add chicken and vegetables, and parsley, and stir until well combined.
Pour filling into very large pie dish or medium baking dish (*or 6 individual baking dishes - see below). Brush outer rim of dish with egg wash. Place pie crust over dish and press edges against rim of dish to adhere. Brush dough with egg wash. With sharp paring knife, cut 4 slits into dough. Place on a rimmed baking pan; bake 1 hour or until top is golden brown and filling is bubbling. Let stand 10 minutes before serving.
**If using individual baking dishes, divide pie crust into 6 pieces and re-shape them the best you can so that they will cover your baking dishes (you may need to use a rolling pin). Proceed with step 4, baking 30 minutes or until top is golden brown and filling is bubbling. Let stand 5 minutes before serving.