In a 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 work the butter into the flour until the mixture resembles coarse crumbs. This creates a flaky texture.

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

Shape the dough into a disk, wrap in plastic wrap, and refrigerate for at least 30 minutes. This allows the gluten to relax, making the dough easier to roll out.

In a skillet, heat 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 vegetables and stir well to coat. This will help thicken the filling.

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

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

Preheat your oven to 400°F (200°C).

On a floured surface, roll out the chilled pie dough to about ⅛ inch thick. Use a round cutter to cut out circles that fit into your muffin tin.

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 remaining dough and cut out smaller circles or shapes to top each pie. Place the tops on the filled pies and crimp the edges to seal.

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

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

Remove from the oven and allow to cool for a few minutes before serving. This helps the filling set slightly, making them easier to eat.