In a large Dutch oven, heat a splash of olive oil over medium heat. Add mushrooms and sauté until browned and tender, about five minutes.
Once the mushrooms are ready, toss in the chopped carrots, celery, and onions. Stir everything together and let it cook for another five to seven minutes.
Sprinkle in the flour and stir well to coat the vegetables. Let it cook for a few minutes to ensure the flour loses its raw taste.
Gradually pour in the unsweetened almond milk, stirring continuously to incorporate it smoothly. Bring to a gentle boil.
Once thickened, fold in the shredded chicken, peas, and fresh thyme. Stir well to combine all the flavors.
Preheat your oven to 425 degrees F. Pour the filling into a pie dish, spreading it evenly.
Roll out your pie crust and place it over the filling. Crimp the edges to seal it, and then brush the top with a beaten egg.
Cut slits in the top of the crust to allow steam to escape.
Bake the Healthy Chicken Pot Pie in the preheated oven for about 25 minutes, or until the crust is golden brown.
Let the pot pie sit for a few minutes before serving. Enjoy!