Preheat oven to 375°F.
To a large pot or Dutch oven over medium heat, add butter. Once melted, add onions and cook until softened, 3-5 minutes. Add garlic and cook for 1 more minute.
Add turkey, potatoes, frozen peas and carrots, and corn. Mix well.
Sprinkle flour evenly over mixture, stirring to coat everything.
Add turkey broth and milk. Simmer, stirring often, until thickened (about 7 minutes).
Add salt, pepper, thyme, and oregano. Stir to combine.
Onto a lightly floured surface, roll out one of the pie crusts into a 12-inch circle. Place into a 9-inch deep dish pie pan, overlapping the sides.
Pour the turkey filling into crust.
Roll out the second pie crust into a 12-inch circle and place it over the filled pie. Seal the edges and trim excess dough. Crimp the edges with your fingers or a fork.
Brush the top crust with the beaten egg.
Using a sharp knife, cut 4-6 small slits into the pie crust for venting.
Bake for 50-55 minutes, or until the top crust is golden brown. Use a pie shield* if the crust is getting too brown around the edges before the pie is done. Let the pot pie rest for 5-10 minutes before serving.