Combine flour and salt. Cut in cold butter until mixture resembles coarse crumbs. Gradually add ice water, mixing until dough forms. Divide in half, wrap in plastic, and refrigerate for 30 minutes.

Melt butter in a skillet. Add onions, carrots, and celery, cooking until tender (about 8 minutes). Stir in flour, then gradually add broth and milk, stirring until thickened.

Add chicken, peas, thyme, salt, and pepper. Simmer for 5 minutes, then remove from heat.

Preheat oven to 425°F (220°C). Roll out one portion of dough and place in a 9-inch pie dish. Pour filling inside. Roll out remaining dough, place over filling, trim, seal, and flute edges. Cut several slits in the top.

Bake for 30-35 minutes until crust is golden brown and filling is bubbling. Let rest for 10-15 minutes before serving.