In a large bowl, mix the flour and salt. Cut in the butter until the mixture resembles coarse crumbs. Gradually stir in the cold water until the dough forms. Divide into two balls, flatten, wrap in plastic, and refrigerate for at least 30 minutes.

Roll Out the Dough

On a floured surface, roll out one dough ball to fit your pie dish. Place it in the dish and trim the edges.

Filling Preparation

Cook the Filling

In a skillet over medium heat, sauté the onion, carrots, and celery until tender. Stir in the flour, then add the chicken broth and milk. Cook until thickened. Add shredded chicken, peas, thyme, salt, and pepper. Remove from heat.

Assembly and Baking

Assemble the Pot Pie

Pour the filling into the prepared crust. Roll out the second dough ball and place it over the filling. Seal the edges and cut slits in the top for steam to escape.

Bake

Preheat the oven to 425°F (220°C). Bake for 30-35 minutes or until the crust is golden brown. Let it cool for a few minutes before serving.