Preheat your oven to 400℉
Heat your large skillet and olive oil over medium heat. Add the mirepoix, cubed potatoes, dried thyme, salt, and black pepper. Cook until softened, 5 minutes.
Lower the heat to medium-low and sprinkle the flour over the vegetables. Stir it all together until all the flour is no longer dry.
Still on medium-low heat, stir in the milk and cook for 2 minutes until it coats everything.
Stir in the chicken stock and raise to medium-high heat until it comes to a simmer, then lower to medium-low and simmer until slightly thickened – about 5-8 minutes. You want it to be able to coat the back of a spoon (this is the sauce/gravy).
Once the sauce is thickened, add the cubed cooked chicken, frozen peas, and fresh parsley to the pot pie filling. Stir to combine.
On a clean surface, roll out the sheet of puff pastry dough using a rolling pin until it is wide enough to cover the circumference of your pan with some extra hang room.
Crack the egg into a small bowl and whisk until scrambled.
Gently place the puff pastry centered over the pot pie, folding the edges on top of themselves.
Evenly brush egg wash over the puff pastry and cut a few slits in the center using a sharp knife to allow air to escape.
Bake the puff pastry chicken pot pie for 20 minutes until the puff pastry is golden brown and puffed.