Combine the all-purpose flour, cake flour, and kosher salt in a large bowl and use a fork to mix them.

Add the cold, diced butter and the chilled shortening to the bowl of flour. Use a pastry cutter to blend the fat into the flour until a crumbly, coarse mixture forms.

Mix the cold water into the flour until a dough ball forms. Don’t worry if there are a few loose crumbles. Use your hands to pull everything together into a dough ball.

Dump the dough onto a large piece of plastic wrap and use your hands to gather any loose crumbs into the dough ball.

Wrap the plastic wrap tightly around the ball of dough. Refrigerate for at least 1 hour or up to 2 days.

While the dough chills, make the pot pie filling. Heat 1 tablespoon extra virgin olive oil in a wide pot over medium heat. Add the diced carrots, celery, and onion. Sauté for 5 to 7 minutes until they soften.

Add the diced potatoes and season with 1 teaspoon kosher salt, a big pinch of black pepper, garlic powder, and dry thyme. Sauté over medium heat for 8 to 10 minutes until the potatoes soften.

Melt the butter into the vegetables. Once bubbly, add the flour and stir to coat. Cook for 2 minutes until the flour becomes nutty and aromatic.

Add half the chicken broth to the pot and whisk to incorporate. Continue whisking until a slurry forms. Add the remaining chicken broth and continue whisking until smooth.

Add the milk and whisk until smooth. Cook over medium heat until bubbly and thick.

Add the freshly grated Gruyère cheese and whisk until melted and smooth. Add the nutmeg and white pepper. Taste and add more salt if needed.

Add the cooked turkey and frozen peas and stir to incorporate. Simmer for 5 minutes until the peas are bright green. Turn off the heat.

Transfer the pot pie filling to a wide dish. Cover loosely with cling wrap and let stand for at least 30 minutes to 1 hour. I recommend transferring it to a wider dish instead of a deep bowl for a more rapid cool-down. See Note 1.

Preheat the oven to 425ºF. Mix the beaten egg and the milk in a bowl and set aside.

Remove the chilled dough from the refrigerator. Cut the ball in half and return half of the dough to the refrigerator. Place the other half on a lightly floured surface and press it into a disc. Use a floured rolling pin to roll the dough into a circle about 1 inch larger than your pie dish.

Carefully lift the dough from the counter and place it into a 9-inch pie dish. See Note 2.

Add another sprinkle of flour to your work surface. Roll out the other half of the dough into a circle about 1 inch larger than the pie dish.

Pour the cooled pot pie filling into the prepared pie dish. Carefully lift the top crust from your surface and place it on top. Trim off any excess and discard it or use it for decoration. Use your fingers to seal the pie crust edges. Crimp the crust with your fingers or a fork if you like. Use a sharp knife to create a few small slits in the top of the crust to allow the steam to escape.

Brush the crust with the egg and milk mixture. You likely won’t use all of it.

Place the pie dish on a large baking sheet. Transfer to the oven for 35 to 40 minutes or until the crust is golden brown and flaky. Rotate the pie once midway through baking for even browning.

Remove from the oven and let stand for 20 minutes.

Cut the pie into 8 slices and transfer to plates. Serve and enjoy!