01 - Set the oven to 400°F to prepare for baking.
02 - In a large skillet over medium heat, melt butter. Add onions, carrots, potatoes, and celery; cook 5 to 7 minutes until softened.
03 - Sprinkle flour over vegetables and stir for 1 minute to fully combine.
04 - Gradually whisk in chicken broth and milk; stir constantly until thick and creamy, approximately 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 - Transfer filling into a 9-inch pie dish.
07 - Roll out pastry to cover the dish. Place over filling, trim excess, seal edges, and cut small slits atop to release steam.
08 - Brush the pastry surface evenly with beaten egg for an appealing golden finish.
09 - Bake for 30 to 35 minutes until crust is golden and filling bubbles.
10 - Allow to rest 10 minutes after baking to set filling.