In a large mixing bowl, whisk together 2 cups of all-purpose flour, 1 tablespoon of granulated sugar, and 1 teaspoon of salt until well combined. Cut in 1 cup of very cold, unsalted butter using a pastry cutter or fork, until the mixture resembles coarse crumbs. Gradually add ice water, one tablespoon at a time, until the dough begins to come together. Shape into a disk, wrap in plastic wrap, and chill in the refrigerator for at least 1 hour.

While the dough chills, preheat your oven to 425°F (220°C).

Once the dough is chilled, remove one disk from the refrigerator and place it on a lightly floured surface. Roll it out to fit your 9-inch pie plate with a thickness of about 1/8 inch. Transfer the rolled dough to the pie plate and place it back in the refrigerator while you prepare the filling.

In a medium saucepan, bring water to a boil and add 1 cup each of diced carrots, frozen corn, and frozen peas. Cook until tender, about 5-7 minutes. Once cooked, drain the vegetables and set aside.

In a large skillet, melt 1/4 cup of unsalted butter over medium heat. Add 1 diced yellow onion and 1 cup of diced celery, cooking until translucent, about 5 minutes. Stir in 2 minced garlic cloves and cook for another minute. Whisk in 1/3 cup of all-purpose flour, salt, black pepper, and a pinch of nutmeg, cooking briefly before gradually adding 2 cups of chicken broth and 1 cup of whole milk. Bring to a simmer until thickened.

Remove the skillet from heat and fold in 2 cups of diced rotisserie chicken and the previously cooked vegetables. Stir until combined. Allow to cool for a few minutes before assembling the pie.

Pour the filling into the chilled pie crust, leveling it with a spatula. Roll out the second disk of crust and lay it over the filling. Trim and seal the edges, then cut a few slits in the top crust for steam to escape, brushing the surface with a beaten egg.

Place the assembled Chicken Pot Pie in the preheated oven and bake for 30-35 minutes, or until the crust is golden brown and the filling is bubbly.

Once baked, let the Chicken Pot Pie cool for about 10-15 minutes. Serve warm.