Preheat the oven to 425 °F (220 °C).

Make the crust: combine flour and salt, cut in cold butter until mixture resembles coarse crumbs, then gradually add cold water until dough comes together. Divide into two disks and chill while preparing filling.

In a large skillet, melt butter over medium heat. Add onion, carrot, celery and garlic — sauté until vegetables soften.

Stir in flour for the sauce; cook 1–2 minutes while stirring. Then slowly add chicken broth and milk (or cream), stirring until sauce thickens and becomes smooth.

Add shredded chicken, peas, salt, pepper, and thyme. Stir to combine. Remove from heat and let mixture cool slightly.

Roll out one dough disk on a floured surface to fit a 9-inch pie dish. Transfer dough into dish. Pour in the chicken filling mixture. Roll out the second dough disk and place on top. Pinch/seal edges and cut a few slits on top to allow steam to escape.

Bake for 45–50 minutes until the crust is golden brown and the filling is bubbling. If edges brown too quickly, cover rim with foil.

Let the pie rest for at least 10–15 minutes before slicing so the filling sets properly.