Preheat your oven to 200°C (180°C fan) / 400°F. Place a 10-inch oven-safe skillet or cast-iron pan over a medium-high heat. Add the butter and let it melt, swirling the pan until it begins to foam and smell nutty.

Sweat the aromatics. Add the chopped onion, carrots, and celery. Cook, stirring occasionally, for about 6-8 minutes. You are looking for the vegetables to soften and the onion to become translucent, and you will smell a sweet, savoury aroma. The carrots should still have a slight bite.

Build the roux. Add the minced garlic and cook for a further minute until fragrant. Sprinkle the flour over the vegetables and stir constantly for 2 minutes. The mixture will look like a thick, sandy paste and will turn a pale golden colour. This step is crucial for removing the raw flour taste.

Whisk in the liquids. Slowly pour in the warm chicken stock, whisking continuously to prevent lumps. Then, add the milk in a steady stream, still whisking. Bring the mixture to a gentle simmer. You will see it thicken from a thin liquid into a glossy, velvety sauce that coats the back of a spoon. This takes about 3-4 minutes.

Finish the filling. Remove the pan from the heat. Stir in the shredded chicken, frozen peas, and thyme. Season generously with salt and pepper. The filling will be thick and creamy, with the chicken and peas distributed throughout the golden sauce. Taste it and adjust the seasoning.

Top with pastry. Unroll your puff pastry sheet on a lightly floured surface. Gently lay the pastry over the skillet, letting the edges overhang slightly. You can crimp the edges with a fork or your fingers for a rustic look. Cut 3-4 small slits in the centre of the pastry to allow steam to escape.

Bake to golden perfection. Brush the top of the pastry with the beaten egg wash. This will give it a beautiful, glossy, deep golden-brown finish. Place the skillet on a baking tray to catch any drips and bake for 25-30 minutes. The pastry should be puffed up, crisp, and a rich shade of golden brown. When you peek through a slit, you will see the filling bubbling gently underneath. Let it rest for 10 minutes before serving.