01 - Preheat the oven to 400°F.
02 - In a large skillet over medium heat, melt the butter. Add onion, carrots, and celery. Cook for 5–6 minutes until softened.
03 - Add garlic and cook for 1 minute more. Stir in diced chicken and cook for 4–5 minutes until just opaque.
04 - Sprinkle in the flour and cook, stirring, for 2 minutes.
05 - Gradually pour in chicken stock, stirring constantly to avoid lumps. Add milk (or cream), bring to a simmer, and cook until thickened (about 4–5 minutes).
06 - Stir in Dijon mustard, thyme, peas, and parsley. Season with salt and pepper. Remove from heat.
07 - Pour the filling into a medium casserole dish or individual ramekins.
08 - Lay the puff pastry over the top, trimming edges to fit. Press down gently and crimp edges if desired. Cut a few small slits in the pastry for steam to escape.
09 - Brush pastry with beaten egg.
10 - Bake for 25–30 minutes or until the pastry is golden brown and filling is bubbling.
11 - Let the pie rest for 5–10 minutes before serving.