If you haven't already, prep your pie crust. You can also use store bought pie crust here for a shortcut! Add the bottom layer into a 9 inch pie dish and set aside.
Melt the butter over medium heat in a large pot. Add in the onion and celery. Saute for about 5 minutes.
Mix in the flour, salt, pepper, thyme and Italian seasoning.
Add in the half and half, chicken broth, bouillon, frozen veggies and chicken.
Mix everything to combine, then reduce the heat to low and let simmer for about five minutes to let the sauce thicken and the flavors combine.
Transfer the filling to the pie dish. Roll out the second half of the dough and add to the top of the filling. Use a fork to seal the edges, or use your thumb and index finger to make indents all the way around. You can also use a knife to make a few slits in the top, but this is just really for decoration!
Whisk the egg in a small dish and use a brush to brush on top of the pie crust.
Bake for 30-35 minutes or until the crust is golden brown. Let cool for about 10 minutes to let the filling set a bit, then garnish with fresh thyme if desired and enjoy!