Preheat the oven to 425º. Heat a large dutch oven or deep skillet on medium-high heat. Add the oil to the skillet. Once it's hot, add the mushrooms and cook for 8 - 10 minutes, until mushrooms are beginning to brown, and sweat. Add the carrots, celery, garlic powder, salt, and pepper. Cook until the carrots begin to soften a bit, about 3-5 minutes.
Sprinkle the all purpose flour over the top of the vegetables, stir in well and cook 2 minutes. Slowly pour in the chicken broth adding a few splashes at a time, stirring constantly, making sure to get all the flour clumps stirred in. Bring the roux to a simmer. Be sure to scrape any brown bits from the bottom of the pan, this will add more flavor. Continue to simmer until thickened, about 3 to 5 minutes. Add in the almond milk, shredded chicken, thawed peas, onions, and fresh thyme. Let it come to a simmer.
Grease a pie dish. or cast iron skillet. Roll the pie dough into a circle large enough to cover your dish. Brush the edges of the pie crust with the egg wash, then lay the dough into the dish. Add the chicken mixture to the pie crust in the dish. Once it is full of the mixture, add the second pie crust to the top of the chicken mixture.
Pinch the sides of the two pie crusts together until it it completely sealed. Slice a few slits around the top of the pie to help vent and distribute heat. Brush with the egg wash (this helps brown the pie crust to a beautiful color). Bake for about 25- 35 minutes or until pie crust is deeply golden and inside it bubbling.
Let it rest for about 5-8 minutes before slicing and serving. Enjoy!