In a mixing bowl, combine flour and salt. Cut in butter until mixture resembles coarse crumbs.

Stir in ice water, a tablespoon at a time, until mixture forms a ball. Wrap in plastic and refrigerate for 30 minutes.

In a skillet, melt butter over medium heat. Add onion, carrots, and celery; cook until softened.

Stir in flour, salt, pepper, and thyme until well combined. Gradually add chicken broth and milk, stirring constantly until thickened.

Add shredded chicken and peas; mix well and remove from heat.

Preheat the oven to 425°F (220°C). Roll out half of the pie crust and fit it into a pie dish.

Pour the filling into the crust. Roll out the second half of the crust and place it over the filling. Seal and cut slits for steam to escape.

Bake for 30-35 minutes or until the crust is golden brown. Let cool for a few minutes before serving.