Preheat oven to 450F. Let half & half come to room temp while you prep your ingredients. Beat egg and set aside.
Rinse and strain frozen mixed vegetables, dice half an onion, and peel and dice a potato.
In a large saucepan, melt ½ stick of butter on medium heat and add diced onion and ¼ tsp salt. Cook until glossy but still firm, about 3 minutes
Add diced potato and cook until par cooked (softened, but still with a little bite), about 7 minutes.
Remove onion and par-cooked potatoes and set aside.
In the same pan on medium low heat, add the remaining ½ stick of butter. Once melted, add flour and whisk to make a light roux.
Add garlic powder, poultry seasoning, remaining ¼ tsp salt, and pepper. Whisk to combine.
To your roux, add chicken broth and half 'n half, keeping the heat at medium low and whisking constantly to keep it smooth.
Once thickened, about 3-4 minutes, remove from heat. Fold in mixed vegetables, diced onion, potato, and parsley.
Then, fold in shredded turkey and parmesan cheese.
Roll one pie crust out in a 9" pie pan. Fill the pie crust with the turkey vegetable filling.
Then, add second crust on top, pinching the top and bottom together.
Cut slits into the top of your pie to let some of the steam escape while cooking, and brush the crust with the previously prepared egg wash.
Wrap the edges with tinfoil gently. Bake for 30 minutes. Then, remove the tinfoil from the crust and finish baking for 10-15 more minutes until the crust is golden brown. Let cool for at least 15 minutes before cutting, or the filling will not set.