Start with the crust: In a large bowl, combine flour, sugar, and salt. Toss in the cold butter cubes until coated.

Roll the butter into the flour using a rolling pin on a clean surface. Continue until the mixture is flaky, then return it to the bowl and chill in the freezer for 15 minutes.

Add cold buttermilk and mix until the dough comes together. Divide into two disks, wrap in plastic, and refrigerate.

Make the filling: Melt butter in a skillet over medium-high heat. Add onions, carrots, celery, and garlic, cooking until tender.

Whisk in flour, salt, pepper, thyme, and parsley. Gradually add chicken broth and heavy cream, whisking until smooth.

Let the mixture simmer until thickened, about 10 minutes. Stir in chicken and peas, then set aside to cool slightly.

Preheat your oven to 400°F. Roll out one disk of dough and fit it into a 9-inch pie pan.

Pour the prepared filling into the crust. Roll out the second disk and place it on top. Crimp the edges and cut slits for venting.

Brush the crust with beaten egg and bake for 45 minutes, shielding the edges with a crust protector if needed.

Let the pie cool for 10 minutes before slicing. Serve warm and enjoy!