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

Gradually add the ice water, 1 tablespoon at a time, mixing until the dough just comes together. Do not overmix. Divide the dough in half, flatten each half into a disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.

In a large skillet or Dutch oven, melt the butter over medium heat. Add the chopped onion, carrots, and celery and cook until softened, about 5-7 minutes.

Stir in the flour and cook for 1 minute, stirring constantly.

Gradually whisk in the chicken broth and milk or cream until smooth. Bring to a simmer and cook, stirring, until the sauce thickens.

Stir in the cooked chicken, frozen peas, salt, and pepper. Remove from heat.

Preheat your oven to 400°F (200°C).

On a lightly floured surface, roll out one disc of dough into a 12-inch circle. Carefully transfer it to a 9-inch pie plate. Trim any excess dough.

Pour the chicken filling into the pie crust.

Roll out the second disc of dough into an 11-inch circle. Place it over the filling. Crimp the edges to seal and cut several vents in the top crust.

Bake for 20 minutes, then reduce oven temperature to 350°F (175°C) and bake for another 20-25 minutes, or until the crust is golden brown and the filling is bubbly.

Let the pot pie cool for at least 10-15 minutes before serving.