Preheat oven to 375 degrees.
In a medium saucepot, melt butter; add onion and sweat 4 minutes. Add celery and carrots; cook 4–5 minutes.
Add turkey, cook 4 minutes. Add tarragon, parsley and all-purpose flour; cook 4 minutes. Add stock and bring to a simmer. Add potatoes and simmer until tender.
Pour filling into pie pan and top with pastry. Brush pastry with egg.
Bake pie 20–30 minutes, or until crust is golden brown.