Preheat your oven to 400°F and place one pie crust in a 9-inch deep dish pie pan, pressing it gently into the bottom and sides.
Melt butter in a large skillet over medium heat, then add onion, carrots, and celery. Cook for about 6-7 minutes until the veggies start to soften.
Stir in the garlic and cook for another minute until fragrant, then sprinkle the flour over everything and stir constantly for about 2 minutes to cook out the raw flour taste.
Slowly pour in the chicken broth and milk, whisking constantly to avoid lumps. Keep stirring until the mixture thickens up nicely, about 5 minutes.
Add the turkey, peas, corn, thyme, salt, and pepper to the creamy mixture, stirring everything together. Let it simmer for 3-4 minutes, then remove from heat.
Pour the turkey filling into your prepared pie crust, spreading it out evenly.
Place the second pie crust over the top, crimp the edges together with a fork (or get creative with your fingers!), and cut 4-5 small slits in the top to let steam escape.
Brush the top crust with the beaten egg for that gorgeous golden color, then bake for 35-45 minutes until the crust is golden brown and the filling is bubbling through the slits.
Let the pot pie cool for 10-15 minutes before slicing—I know it's hard to wait, but trust me, it's worth it!