Preheat your oven to 400°F (200°C) to prepare for the baking process.

In a large skillet, melt 2 tablespoons of unsalted butter over medium heat. Add 2 sliced large leeks and sauté for 5-7 minutes.

Sprinkle 2 tablespoons of all-purpose flour over the softened leeks, stirring well to combine. Cook for an additional minute.

Gradually whisk in 1 cup of chicken broth, stirring continuously until the mixture thickens.

Reduce the heat to low and stir in 1 cup of heavy cream, 1 teaspoon of Dijon mustard, 1 tablespoon of fresh thyme, and salt and pepper to taste.

Add 2 cups of diced cooked chicken to the creamy mixture and stir well until coated.

Press one sheet of puff pastry into your 9-inch pie dish, trimming any excess.

Carefully pour the cooled chicken and leek filling into the prepared crust, spreading it out evenly.

Place the second sheet of puff pastry over the top, sealing edges by crimping with a fork, and cut slits for steam.

Brush the top crust with a beaten egg for a glossy finish.

Place the pie on a baking sheet and bake for 25-30 minutes until golden brown.

Once baked, let the pie cool for at least 10 minutes before slicing.