In a large mixing bowl, combine the flour and salt. This helps to evenly distribute the salt throughout the dough.

Add the cold, cubed butter to the flour mixture. Use a pastry cutter or your fingers to mix until the mixture resembles coarse crumbs. This step is crucial for creating a flaky crust.

Gradually add the ice water, one tablespoon at a time, mixing until the dough comes together. Be careful not to overwork the dough.

Divide the dough into two equal parts, shape them into discs, wrap in plastic wrap, and refrigerate for at least 30 minutes.

In a saucepan, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 3-4 minutes.

Stir in the mixed vegetables and cook for an additional 2-3 minutes until heated through.

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

Slowly pour in the chicken broth while whisking to prevent lumps. Bring to a simmer and cook until slightly thickened, about 5 minutes.

Add the heavy cream, cooked chicken, thyme, garlic powder, salt, and pepper. Stir to combine and remove from heat. Allow to cool slightly.

Preheat your oven to 400°F (200°C).

Roll out one disc of dough on a floured surface to about ⅛ inch thick. Cut out circles that are slightly larger than the muffin tin cups.

Gently press the dough circles into the muffin tin cups, ensuring they cover the bottom and sides.

Fill each crust with the chicken filling, being careful not to overfill.

Roll out the second disc of dough and cut out smaller circles to place on top of the filling. Seal the edges by crimping with a fork.

In a small bowl, whisk together the egg and water to create an egg wash. Brush the tops of the pies with the egg wash for a golden finish.

Bake in the preheated oven for 20-25 minutes, or until the crust is golden brown and the filling is bubbly.

Remove from the oven and let cool for a few minutes before serving. This allows the filling to set slightly.