1-First, preheat your oven to 375 degrees Fahrenheit and prepare your ingredients by combining the potatoes, carrots, peas, and 2 cups of chicken broth or stock in a large saucepan. Bring it to a boil and cook for 10 to 15 minutes until the potatoes are fork-tender, then drain and set aside.

2-Next, in another saucepan, heat 1 tablespoon of olive oil over medium heat. Add 1/4 cup of finely chopped yellow onion and cook for 2 to 3 minutes, then stir in 2 cloves of minced garlic and cook for 30 seconds. Add 1/2 cup of thinly sliced celery and cook until it’s soft and translucent, then mix this with the boiled vegetables.

3-Return the saucepan to the stove and melt 1/3 cup of unsalted butter. Whisk in 1/3 cup of all-purpose flour and cook until it turns light brown, about 3 to 4 minutes. Season with salt, pepper, 1/4 teaspoon celery seed, 1/4 teaspoon dried thyme, 1 teaspoon Italian seasoning, and 1 tablespoon minced fresh flat-leaf parsley.

4-Gradually add 1-3/4 cups of chicken stock or broth and 2/3 cup of whole milk, then simmer on medium-low heat until the sauce thickens, stirring often. This step creates the creamy base that makes the pie so irresistible.

5-Stir in 1 cup of frozen corn, 1-1/2 cups of cubed pre-baked honey ham, and the cooked vegetable mixture. Taste and adjust seasoning as needed to get those flavors just right.

6-Place one unbaked 9-inch pie crust in a 9-inch deep dish pie pan and brush it lightly with the egg whites from 1 large egg. Prebake for 5 minutes to set the base.

7-Add the filling to the pie pan, cover with the second unbaked 9-inch pie crust, seal the edges, cut slits on top for steam, and brush with the remaining egg whites. Bake for 35 to 40 minutes until the crust is golden brown, covering edges if they brown too quickly.

8-Finally, let the pie cool for 10 minutes before slicing, and garnish with fresh thyme or parsley if you like. For dietary changes, use alternatives like vegan butter to keep it simple and adaptable.