Step 1: Prepare the Dough

1. In a mixing bowl, combine flour and salt.

2. Cut in the butter using a pastry cutter or hands until it resembles coarse crumbs.

3. Slowly add ice water, mixing until the dough comes together.

4. Divide into two disks, wrap in plastic wrap, and chill for 30 minutes.

Step 2: Make the Filling

1. Melt butter in a large skillet over medium heat.

2. Add onions, carrots, and celery, sauté until softened.

3. Stir in flour and cook for 1 minute.

4. Gradually add chicken broth and milk, whisking until thickened.

5. Add shredded chicken, peas, and seasonings; mix well.

Step 3: Assemble the Pie

1. Roll out one dough disk and place it in a 9-inch pie dish.

2. Pour the filling evenly into the crust.

3. Roll out the second dough disk and place it over the filling.

4. Seal the edges, crimp with a fork, and cut slits on top for steam to escape.

Step 4: Bake the Pie

1. Preheat the oven to 375°F (190°C).

2. Brush the top crust with an egg wash for a golden finish.

3. Bake for 35-40 minutes or until golden brown.

Step 5: Let It Rest and Serve

1. Allow the pie to cool for 10 minutes before slicing.

2. Serve warm and enjoy!