In a large bowl, whisk together flour, sugar, and salt.

Add the cold butter cubes and gently toss to coat.

Using a rolling pin, press the butter into thin flakes, mixing with the flour until the texture is coarse and crumbly.

Gather the mixture into a pile, return it to the bowl, and place it in the freezer for 15 minutes.

Once chilled, add cold buttermilk and mix gently until the dough starts to hold together.

If needed, drizzle in cold water one tablespoon at a time until it forms a shaggy dough.

Divide into two disks, wrap each in plastic, and refrigerate while you make the filling.

In a large skillet, melt the butter over medium heat.

Add onion, carrots, and celery, cooking for 5–7 minutes until softened.

Stir in the minced garlic and cook for 1 minute more until fragrant.

Sprinkle flour over the cooked vegetables and stir continuously for 1–2 minutes.

Gradually pour in chicken broth, whisking to remove any lumps.

Add heavy cream, thyme, parsley, salt, and pepper.

Simmer for 8–10 minutes over low heat until thickened and smooth.

Add shredded chicken (or turkey) and frozen peas to the sauce.

Stir until everything is evenly coated and creamy.

Remove from heat and set aside to cool slightly while you prepare the crust.

Preheat the oven to 400°F (200°C).

On a lightly floured surface, roll out one disk of dough into a 12-inch circle, about ¼ inch thick.

Fit it into a 9-inch pie pan and trim the excess edges.

Spoon the chicken filling into the crust and spread evenly.

Roll out the second dough disk and place it over the filling.

Trim, seal, and crimp the edges with your fingers or a fork.

Cut a few small slits in the top to allow steam to escape.

Brush the entire crust with beaten egg for a glossy golden finish.

Bake for 45 minutes, or until the crust is beautifully golden and crisp.

If the edges brown too quickly, cover them loosely with foil.

Let cool for 10–15 minutes before slicing to help the filling set.