Preheat oven to 400°F.
Heat olive oil in heavy large skillet over medium-high heat.
Add chopped onion, carrots and celery and sauté until browned.
Add sliced mushrooms and sauté until browned and caramelized, about 4 minutes.
Add diced turkey, gravy, and thyme.
Bring filling mixture to simmer.
Season to taste with kosher salt and freshly ground pepper.
Mix in peas and chopped parsley.
Pour filling into 9-inch-deep dish pie tin.
Lay out prepared pie crust and cut out vent holes. (Simple slashes or decorations like leaves). Place crust on top filling and pinch edges of crust all around. Brush with egg wash.
Bake turkey pot pie until crust is golden and filling is bubbling, 30 - 35 minutes.
Remove and let cool slightly before serving.
Serve with cranberry sauce.