In a large skillet, heat the olive oil over medium heat. Add the chopped onion and garlic, and sauté until the onion is translucent, about 3-4 minutes.

Add the diced chicken to the skillet and cook until browned and cooked through, about 5-7 minutes. Stir occasionally to ensure even cooking.

Once the chicken is cooked, add the carrots, celery, and peas. Cook for an additional 5 minutes until the vegetables are tender.

Sprinkle the flour over the mixture and stir well to coat. This will help thicken the filling.

Gradually whisk in the chicken broth and milk, stirring constantly to avoid lumps. Bring the mixture to a simmer and cook until it thickens, about 3-5 minutes.

Stir in the thyme, salt, and pepper. Remove from heat and set aside to cool slightly.

In a mixing bowl, combine the whole wheat flour and salt. Add the cold butter pieces and use a pastry cutter or your fingers to mix until the mixture resembles coarse crumbs.

Gradually add the cold water, mixing until the dough comes together. If the dough is too dry, add a little more water, one tablespoon at a time.

Form the dough into a ball, wrap it in plastic wrap, and refrigerate for at least 15 minutes.

Preheat your oven to 400°F (200°C).

On a floured surface, roll out the chilled dough to fit your 9-inch pie dish. Place the rolled dough into the dish and trim any excess.

Pour the chicken filling into the crust, spreading it evenly.

Roll out the remaining dough for the top crust and place it over the filling. Seal the edges by crimping with a fork or your fingers. Cut a few slits in the top to allow steam to escape.

Bake in the preheated oven for 25-30 minutes, or until the crust is golden brown.

Let the pot pie cool for about 10 minutes before serving. This allows the filling to set slightly.