01 - Preheat oven to 400°F (200°C).
02 - Melt butter in a large skillet over medium heat. Add onions, carrots, potatoes, and celery. Sauté for 5 to 7 minutes until softened.
03 - Sprinkle flour over vegetables and stir continuously for 1 minute to combine.
04 - Gradually whisk in chicken broth and milk. Stir continuously until sauce thickens and becomes creamy, about 3 to 5 minutes.
05 - Stir in cooked chicken, peas, salt, pepper, thyme, and optional sage. Simmer gently for 3 minutes, then remove from heat.
06 - Pour filling into a 9-inch pie dish or equivalent baking dish.
07 - Roll out pastry to fit over the dish. Lay it over filling, trim excess, seal edges, and cut slits on top for steam release.
08 - Brush pastry surface with beaten egg to achieve golden finish.
09 - Bake for 30 to 35 minutes, until crust is golden brown and filling bubbles.
10 - Allow to rest for 10 minutes before slicing and serving.