For the Pie Crust:

1. In a medium-sized mixing bowl whisk together the flours, xanthan gum, and salt.
2. Add the butter and using a pastry cutter or 2 knives cut the butter into the flours until it looks like very coarse crumbs with some large chunks of butter about the size of your fingernail(see picture).
3. Add the apple cider vinegar, and then add the ice water 1 tablespoon at a time, mixing lightly with a fork until it starts to pull together into a crumbly looking dough. If you pinch in between your fingers it should easily come together into a dough. It took me 4 Tablespoon of water, but depending on your climate, your flour, and the weather you might need more.
4. Divide the mixture in half and dump each half onto a large square of plastic wrap, and use the plastic wrap to form the dough into a disc, handling it as little as possible.
5. Wrap the discs tightly in the plastic wrap and let it rest in the fridge for 30 minutes. (Don't let it rest much longer, it will dry out.)
6. Roll out the first disc of dough between 2 large pieces of plastic wrap or parchment paper until it is 1/8-1/4" thick.
7. Remove the top sheet of plastic wrap and transfer the crust to a 9-inch pie pan by lifting the crust up using the bottom sheet of plastic wrap, and then flipping it over into the pan. Gently press the crust into the corners of the pan, repair any tears, and then trim the edges.

For the Filling:

1. Heat a large heavy bottomed pot over medium-high heat. Season the chicken generously with salt and pepper, drizzle the oil in the pan, and cook the chicken, turning half way through. Remove the chicken from the pan to cool, and then once cooled cut it into bite-sized pieces and set aside for later.
2. Add the butter to the pot and melt. Then add the celery, carrots, and onions. Sauté until the onions have just started to turn translucent (about 10 minutes.)
3. Add the potatoes and continue to sauté until the potatoes are soft, about another 10 minutes.
4. Sprinkle the flour over the vegetable and cook while stirring for about 10 minutes. The flour may just start to turn golden in parts.
5. Add the broth and the milk and bring to a boil while stirring. Let it continue to boil until it is thickened.
6. Turn off the heat, add the frozen peas and the cooked chicken, and season to taste with salt and pepper.

To Bake the Pie:

1. Preheat oven to 375°F.
2. Fill the crust with the filling and roll the second disc of dough out just like the first, placing it gently over the filling. Trim the edges and then crimp as desired. Cut a few slices into the top of the crust to allow steam to escape.
3. Bake for 50-60 minutes, or until the crust is starting to turn a nice golden brown.
4. Let cool slightly before cutting.