Preheat the oven to 450°F.
In a medium saucepan, melt the butter over medium heat. Add the diced onions and saute until the onion is translucent, about 3 to 4 minutes.
Add the flour, salt, and pepper. Cook, stirring constantly until the flour mixture begins to brown, about 3 to 4 minutes.
Slowly stir or whisk the chicken broth and whole milk into the flour mixture. Stir constantly while pouring just a bit at a time to make a smooth mixture
Continue cooking over medium heat, stirring constantly to ensure the milk does not burn on the bottom of the pan. Cook until the mixture begins to bubble and thicken slightly, about 5 minutes. Remove from the heat.
Stir in the cream cheese, frozen vegetables, and diced chicken. Stir to mix evenly. Set aside.
Prepare the pie crusts, fitting the bottom crust into a 9-inch pie plate with edges hanging over for crimping in the next step.
Spoon the chicken pot pie filling into the pie crust, spreading evenly. Place the top crust over the filling.
Fold under the overhanging edges so that the top and bottom crusts come together and seal at the edges. Crimp.
Brush the top of the pie with egg yolk mixture and slit the top in a few places for venting.
Bake for 15 minutes in the 450°F oven. Check pie for a deep golden brown. When it is browned to your preference, cover with aluminum foil and continue baking 15 minutes longer until the bottom crust is also cooked and th filling is bubbling up under the crust.
Cool for at least 15 minutes before cutting and serving.