Make the Filling:

1. Cook the vegetables:
   In a large skillet, heat olive oil over medium heat. Add onion, carrots, and potatoes. Cook for about 5–7 minutes until vegetables start to soften.

2. Add garlic and spices:
   Stir in the garlic, paprika, cumin, and chili powder, and cook for another 1–2 minutes until fragrant.

3. Create the sauce:
   Sprinkle the flour over the vegetables and stir well to coat. Gradually add chicken broth, stirring constantly to avoid lumps. Once the broth is incorporated, pour in the cream and continue stirring until the mixture thickens (about 3–5 minutes). Season with salt and pepper.

4. Add chicken and peas:
   Stir in the shredded chicken and frozen peas. Cook for another 2–3 minutes to combine and heat through. Remove from heat and set aside.

Make the Crust:

1. Prepare the dough:
   In a large bowl, combine flour and salt. Cut in the cold butter with a pastry cutter or two forks until the mixture resembles coarse crumbs. Gradually add cold water, 1 tablespoon at a time, until the dough just comes together.

2. Chill the dough:
   Form the dough into a disk, wrap in plastic, and chill in the refrigerator for at least 30 minutes.

Assemble the Pot Pie:

1. Preheat oven:
   Preheat the oven to 375°F (190°C).

2. Roll out the dough:
   On a floured surface, roll out the dough to fit a 9-inch pie dish. Press it gently into the dish, and trim any excess around the edges.

3. Fill the pie:
   Pour the chicken mixture into the prepared pie crust.

4. Top with crust:
   Roll out the second half of the dough and place it on top of the pie, sealing the edges. Cut a few small slits in the top to allow steam to escape.

5. Egg wash:
   Brush the top crust with a beaten egg to give it a golden, glossy finish.

6. Bake the pie:
   Bake in the preheated oven for 35–40 minutes or until the crust is golden brown. If the edges brown too quickly, cover them with foil during the last few minutes of baking.

7. Rest and serve:
   Let the pie rest for 10 minutes before slicing and serving.