In a large bowl, whisk together flour and salt. Cut in cold butter with a pastry blender or your fingertips until mixture resembles coarse crumbs.

Gradually add ice water, 1 tablespoon at a time, mixing until dough just comes together. Divide dough in half, flatten into discs, wrap in plastic wrap, and refrigerate for at least 30 minutes.

Melt butter in a large skillet or Dutch oven over medium heat. Add onion, carrots, and celery and cook until softened, about 8-10 minutes.

Stir in flour and cook for 1 minute. Gradually whisk in chicken broth and milk until smooth. Bring to a simmer, stirring constantly, until thickened.

Stir in peas, corn, shredded turkey, salt, pepper, and thyme. Cook for 2-3 minutes until heated through. Remove from heat.

Preheat oven to 400°F (200°C).

On a lightly floured surface, roll out one disc of dough into a 12-inch circle. Carefully place it into a 9-inch pie plate.

Pour the turkey filling into the pie crust.

Roll out the second disc of dough. Place it over the filling. Trim and crimp the edges to seal. Cut several slits in the top crust to allow steam to escape.

Bake for 20 minutes, then reduce oven temperature to 375°F (190°C) and bake for another 20-25 minutes, or until crust is golden brown and filling is bubbly.

Let stand for 10 minutes before serving.