Heat a splash of oil in a large skillet over medium heat. Add the sliced leeks and sauté for about 5 minutes, stirring occasionally until they soften and turn a delicate golden color.

Add the cubed chicken thighs to the pan with the softened leeks. Cook for approximately 7-10 minutes, stirring frequently, until the chicken is browned on all sides and no longer pink in the center.

In the same skillet, melt 2 tablespoons of butter over low heat. Stir in the plain flour, cooking for 1 minute to create a roux.

Gradually whisk in the chicken stock while you continue to stir, ensuring there are no lumps. Increase the heat to medium and cook for about 2-3 minutes until the sauce thickens.

Lower the heat and stir in the double cream and chopped fresh tarragon. Season with salt and pepper to taste.

Spoon the creamy chicken and leek mixture into a pie dish, spreading it evenly. Preheat your oven to 200°C (fan 180°C, gas 6).

Roll out the ready-rolled puff pastry and gently place it over the filled pie dish, crimping the edges to seal. Cut a few steam vents in the center.

Brush the top of the pastry with a beaten egg and place the pie in the preheated oven. Bake for 25-30 minutes, or until the pastry is puffed and golden brown.