Prepare Ingredients: Preheat your oven to 400°F (200°C). Dice the chicken breasts into bite-sized pieces and thinly slice the leeks.

Cook the Chicken and Leeks: In a large skillet or saucepan, heat the butter and olive oil over medium heat. Introduce the chicken pieces to the pan, seasoning them generously with salt and pepper. Sauté until the chicken is golden brown all over, roughly 5 to 7 minutes. Once browned, take the chicken out of the pan and set it aside for later use. In the same pan, add the sliced leeks and cook until soft and fragrant, about 5 minutes. Add the garlic and cook for an additional 1-2 minutes.

Create the Creamy Sauce: Return the chicken to the pan with the leeks and garlic. Pour in the white wine, stirring to combine, and let it simmer for 5 minutes until slightly reduced. In a separate small bowl, combine the cornflour with water to form a smooth slurry. Pour this mixture into the pan, stirring steadily until the sauce begins to thicken. Incorporate the double cream and mascarpone cheese, continuing to cook until the blend is rich and velvety. Adjust the seasoning with extra salt and pepper as needed. To finish, fold in the chopped parsley and mix thoroughly.

Assemble the Pie: Pour the creamy chicken and leek mixture into a baking dish. Roll out the puff pastry sheet and lay it over the filling, trimming any excess around the edges. Crimp the edges of the pastry to seal, and brush the top with the beaten egg for a golden finish. Make several small cuts in the pastry to let steam vent while it bakes.

Bake: Transfer the pie to the preheated oven and bake for 25 to 30 minutes, or until the pastry turns a beautiful golden brown and puffs up, with the filling bubbling delightfully.

Serve and Enjoy: Remove the pie from the oven and let it cool slightly before serving. Garnish with a bit more parsley if desired.