Preheat oven to 375 degrees F. In a large saucepan, combine the cut potatoes, carrots, and peas. Cover with 2 cups chicken stock and then boil for 10-15 minutes or until potatoes are fork tender. Remove from heat, drain and set aside.
In a large saucepan over medium heat, add the olive oil. Once shimmering, add in the onion and cook for 2-3 minutes and then add in the garlic. Cook for 30 seconds and then add in the celery. Stir until soft and translucent. Transfer this mixture right on top of the other veggies. Return the saucepan and add in the butter. Once melted, whisk into the flour and whisk for 3-4 minutes until the mixture is a light brown (adds tons of flavor). Season with salt and pepper to taste, celery seed, Italian seasoning, thyme, and Italian parsley. Slowly stir in chicken broth and milk. Simmer over medium-low heat until thick (if you like a thinner sauce, add more chicken broth and milk a little at a time until you reach your desired consistency). Add the corn and cubed ham to the other veggies and then combine the veggies with the sauce. Stir until combined. Taste and adjust seasonings (add more salt/pepper/spices as needed to preference).
Place one of the pie crusts in a 9” pie pan (use a deep-dish pie pan if you have one) and lightly brush with egg whites. Bake in the oven for about 5 minutes, remove, and pour in the sauce/veggie mix. Cover with the other crust and seal the edges. Cut some slits in the top, brush with egg whites and bake for about 35-40 minutes or until the crust is golden brown.
Serve if desired with fresh thyme/and or parsley.