Preheat oven to 350 degrees.
Start by finely cutting up the celery, carrots, and onion.
In a cast-iron skillet or large pan, melt the butter (can use non-dairy) over medium heat. Add the celery, carrot, onion, and peas. Saute about 5 minutes, or until veggies start to soften.
Add the chicken, coconut milk, chicken broth, salt, pepper, and thyme. Taste and adjust seasonings. Bring to boil.
Allow to gently boil for 10 - 15 minutes or until thickened, stirring occasionally. If not using a cast-iron skillet transfer to a deep pie pan. Set aside.
Place the pie crust on a large piece of parchment paper and cover with plastic wrap. Roll out from the center using a rolling pin. Invert over the pot pie and gently press into the sides of the dish to seal, patching up any cracks with your fingers.
Brush the top with a beaten egg (optional). Bake for 20 minutes or until the crust is golden brown and the filling is bubbly.
Use a large spoon to serve.