1. Melt butter in a large skillet over medium heat and cook onion until translucent.

2. Add diced potatoes and mixed vegetables and sauté for 3 to 4 minutes.

3. Sprinkle flour over the vegetables and stir constantly to form a roux.

4. Gradually whisk in chicken broth and milk or cream, bringing the mixture to a gentle simmer until thickened.

5. Stir in shredded chicken and season with salt and black pepper, then simmer for 2 minutes and remove from heat to cool slightly.

6. Fit one pie crust into a 9-inch pie dish and pour in the cooled filling.

7. Cover with the second crust, trim edges, crimp to seal, and cut slits for steam to escape.

8. Brush with egg wash if desired and bake at 400°F for 30 to 35 minutes until the crust is golden and filling bubbles.

9. Let the pie rest for 10 minutes before slicing and serving.