Preheat the oven to 200°C (400°F/Gas 6). Lightly flour a work surface and have a 20–23cm pie dish ready.
Trim and thinly slice the Leek (white and pale green only) and pat dry. Cut the Chicken Thighs into bite-sized pieces and season with a little Salt and Black Pepper.
Heat a large frying pan over medium-high heat, add a splash of Olive Oil and a knob of Butter. When hot, brown the chicken in batches until golden on all sides, then transfer to a plate and set aside.
Reduce the heat to medium, add a little more Butter or Olive Oil if needed and gently sweat the Leek until softened and slightly caramelised, about 6–8 minutes.
Stir in the Plain Flour and cook for 1–2 minutes to remove the raw flour taste, then gradually whisk in the Chicken Stock, scraping any browned bits from the pan to make a smooth sauce.
Add the Double Cream, stir in the Dijon Mustard, tuck in a sprig or two of Thyme and the Bay Leaf, then return the browned chicken to the pan. Simmer gently until the chicken is cooked through and the sauce is thick and glossy.
Taste and adjust seasoning with more Salt and Black Pepper as needed. Remove the Bay Leaf and any woody thyme stems, then allow the filling to cool slightly so it will not steam the pastry.
Line the pie dish with one sheet of Ready-Rolled Puff Pastry, trimming any excess, then spoon in the cooled chicken and leek filling. Top with the second sheet of Ready-Rolled Puff Pastry, trim and crimp the edges to seal, and cut a couple of small vents in the top.
Beat the Egg and brush it over the pastry to give a glossy, golden finish. Chill for 10 minutes if the pastry has softened while assembling.
Bake in the preheated oven for 25–35 minutes, or until the pastry is puffed and deep golden and the filling is bubbling. Rest the pie for 10 minutes before slicing and serving.
