Melt the Butter in a Large Skillet pan on a low heat, add the Diced Onion and cook for 5 minutes on a medium-low heat.
Add the Flour, Poultry Seasoning, Thyme, Salt and Pepper. Cook for another 2 minutes.
Whisk in the Chicken Broth, and Whole Milk or Cream a little at a time, stirring thoroughly with each addition. May seem thick at first, it will smooth out. Simmer for 1 minute once all combined.
Stir in the Diced Turkey (or Chicken) and Vegetables.
Add this mixture to the prepared Pie Plate.
Roll out the top crust into a circle shape and place on to the top of the filling. Pinch the edges shut. Cut a few slits into the top pie crust to vent pie.
Whisk together the Egg and 1 Tbsp. of water in a small bowl. Brush the egg mixture onto the top crust of the prepared pie.
Bake the pie for 35-40 minutes, until the crust is lightly browned.
Allow the pie to cool for 10 minutes before cutting. Enjoy!