CRUST: 

1. Combine the flour, salt, and cold butter in a medium-sized bowl. Incorporate the ingredients using your hands until it forms a crumbly mixture.
2. Add the cold water and incorporate until the dough forms. Separate into two sections, and create 2 small discs with your hands, sort of like a hamburger patty. Place in the fridge while you make the filling. Resume with step 3 (Crust) once steps 1 - 5 (Filling) are completed.
3. Flour a counter surface, and start to roll out both dough discs into two separate 12-inch discs. Sprinkle more flour over the dough as needed if it seems too wet.
4. Lightly fold one of the dough discs into 4 quarters without pressing firmly to help transfer the dough to an ungreased pie dish (9-inch round dish).
5. Resume step 7 (filling).

FILLING:

1. In a large frying pan on medium heat, add the olive oil, onions, celery, and mushrooms. Fry until onions are translucent and celery and mushrooms are soft - about 10-15 minutes.
2. Add the minced garlic, cook for 1 minute.
3. Add the vegetable medley and half the salt and pepper. Cook until vegetables are no longer frozen, about 5 minutes.
4. Move all the veggies to the sides of the pan. Add 1 tablespoon of olive oil to the middle of the pan and add the cubed chicken. Cook until no longer pink - about 5 minutes. Incorporate the vegetable mixture with the chicken in the pan. Turn off heat.
5. Preheat the oven to 425° F or 220° C.
6. Resume making the crust (Step 3 (Crust)).
7. Pour the chicken and vegetable mixture into the crust that’s lining the pie dish.
8. Combine the flour, remaining salt and pepper, and dried thyme in a small bowl.
9. In the same pan that you cooked the chicken and vegetables in, add the butter, flour mixture from step 8, chicken broth and milk. Simmer and constantly stir on low to high heat, until it starts to thicken and become creamy, about 5 minutes.
10. Pour over chicken and vegetable mixture.
11. Place the final dough disc on top to seal the pie. Pinch the edges of the pie dough and trim away excess dough as desired.
12. Beat 1 egg, and brush the pie dough.
13. Poke many holes in the top crust using a fork or knife to allow steam to escape.
14. Bake for 30 - 35 minutes, uncovered.
15. Cool at room temperature for 5 minutes before serving.