In a large mixing bowl, whisk together 2½ cups ⅓ cup all-purpose flour, 1 tsp 1 tsp kosher salt, and 1 tsp 1 tsp granulated sugar. Add the cold 4 tbsp unsalted butter cubes and use your fingertips to work the 4 tbsp unsalted butter into the ⅓ cup all-purpose flour until the mixture resembles coarse crumbs with some pea-sized pieces remaining — this creates flakiness.

Drizzle in ice water one tablespoon at a time, tossing gently with a fork after each addition, until the dough just comes together and holds when pinched. You may not need all the ice water added 1 tbsp at a time. Do not overwork the dough.

Divide the dough into two equal discs, wrap each tightly in plastic wrap, and refrigerate for at least 30 minutes (or up to 2 days). Cold dough is much easier to roll and produces a flakier crust.

Melt 4 tablespoons of unsalted butter in a large skillet over medium-high heat. Season the 1 ½ lb boneless skinless chicken breasts cut into 3/4-inch cubes cubes with a pinch of kosher salt and ½ tsp black pepper freshly ground, then add them to the skillet in a single layer. Cook for 4–5 minutes, stirring occasionally, until lightly golden and just cooked through. Transfer the 1 ½ lb boneless skinless chicken breasts cut into 3/4-inch cubes to a plate and set aside.

In the same skillet over medium heat, add the diced yellow onion diced, 3 stalks celery sliced, and 3 medium carrots peeled and diced. Sauté for 6–7 minutes, stirring occasionally, until the vegetables are softened. Add the 3 cloves garlic minced and 1 tsp fresh thyme leaves and cook for 1 more minute until fragrant.

Sprinkle the ⅓ cup all-purpose flour over the vegetables and stir well to coat everything evenly. Cook for 1–2 minutes to eliminate the raw ⅓ cup all-purpose flour taste.

Slowly pour in the 2 cups chicken broth low-sodium preferred while whisking constantly to prevent lumps. Then add the ¾ cup whole milk and ¼ cup heavy cream. Bring the mixture to a gentle simmer over medium heat, stirring frequently, and cook for 4–5 minutes until the sauce thickens enough to coat the back of a spoon.

Remove the skillet from the heat. Stir in the cooked 1 ½ lb boneless skinless chicken breasts cut into 3/4-inch cubes and 1 cup frozen peas no need to thaw. Taste and adjust seasoning with 1 tsp kosher salt and ½ tsp black pepper freshly ground as needed. Let the filling cool slightly while you roll out the crust — a slightly cooled filling prevents the bottom crust from getting soggy.

Preheat your oven to 425°F. On a lightly floured surface, roll one disc of dough into a 12-inch circle. Carefully transfer it to a 9-inch pie dish, pressing it gently into the bottom and sides. Let any excess hang over the edge.

Pour the filling into the prepared crust, spreading it into an even layer. Roll out the second disc of dough into another 12-inch circle and lay it over the filling. Trim any excess dough to about a 1-inch overhang, then fold the edges under and crimp them together firmly with your fingers or a fork to seal.

In a small mixing bowl, whisk together the 1 egg and 1 tablespoon of whole milk to make the egg wash. Brush the egg wash evenly over the top crust. Cut 4–5 small slits in the center of the top crust to allow steam to escape during baking.

Place the pie dish on a baking sheet to catch any drips. Bake at 425°F for 30–35 minutes, until the crust is deep golden brown and the filling is bubbling through the vents. If the edges begin to brown too quickly, cover them loosely with strips of aluminum foil after the first 20 minutes.

Remove from the oven and let the pot pie rest for 10–15 minutes before slicing. This allows the filling to set slightly so it holds together when served.