Preheat your oven to 400°F (200°C).

In a large skillet, heat the olive oil over medium-high heat. Add the chopped chicken thighs and cook until browned on all sides, about 5 to 7 minutes. Remove the chicken from the skillet and set aside.

In the same skillet, melt the butter over medium heat. Add the sliced leeks, quartered mushrooms, and diced potatoes. Sauté for about 8 minutes, or until the leeks have softened and the potatoes begin to turn tender.

Sprinkle the all-purpose flour evenly over the vegetables. Stir continuously for 2 minutes to cook out the raw flour taste.

Gradually whisk in the chicken stock and heavy cream, ensuring there are no lumps. Bring the mixture to a gentle simmer and cook for 5 to 10 minutes until the sauce thickens and coats the back of a spoon.

Stir the browned chicken and the chopped wild garlic leaves into the creamy sauce. Season generously with salt and black pepper. Remove the skillet from the heat.

Pour the chicken, vegetable, and wild garlic filling into a 9-inch pie dish, spreading it out in an even layer.

Unroll the thawed puff pastry sheet and drape it over the pie dish. Crimp the edges tightly to seal the pie. Cut three small slits in the center of the pastry to allow steam to escape.

Brush the entire surface of the puff pastry evenly with the beaten egg.

Bake in the preheated oven for 25 to 30 minutes, or until the pastry is puffed and golden brown, and the filling is bubbling around the edges. Allow the pie to cool for 10 minutes before slicing and serving.