In a large skillet or pan set over medium-high heat, add a splash of olive oil then add the onion, celery and carrots.
Allow to sauté for a few minutes until the vegetables are soft and golden brown. Add the garlic and cook for another minute then season with dried thyme, garlic powder, salt and black pepper.
Transfer the vegetables to a large mixing bowl.
Add the shredded chicken, béchamel sauce and frozen peas.
Stir together, taste and adjust seasoning if necessary.
Transfer the filling to a baking dish (the one I used was approximately 9x13inches/22x33cm).
Roll the puff pastry out on a floured surface into a rectangle big enough to fit your dish.
Top the filling with the pastry, crimp the edges and brush the top with beaten egg.
Place the pot pie in the preheated oven and allow to bake for 20-25 minutes until the puff pastry is crisp and golden.
Remove from the oven and allow to rest for a few minutes before serving.