Place almond flour, coconut flour, seasonings, and xanthan gum in a bowl in the freezer for 15 minutes.
Add the chilled mixture to a food processor with butter, and cream cheese. Pulse until it forms large pea-sized crumbs.
Add egg and pulse until the mixture forms a dough.
Refrigerate the dough 2 hours or overnight.
Filling
In a small saucepan, cover diced turnips with water and bring to a boil. Simmer covered until tender, about 7 minutes. Drain well.
In a large saucepan over medium heat, melt butter. Add onion, garlic, poultry seasoning, thyme and cook until softened, about 3-4 minutes. Add celery, mushrooms and carrots and cook until tender, about 5-6 minutes more.
In a small bowl, whisk Xanthan gum with ½ cup broth.
Add remaining broth to vegetable mixture and bring to a boil. Whisk in Xanthan gum mixture until thickened. Stir in heavy cream. Simmer 5 minutes.
Stir in turnips, chicken and parsley. Taste and season with salt and pepper.
Assembly
Preheat the oven to 400°F. Grease a 9" pie plate.
Roll half of the dough into a 12" circle between parchment paper. Line the bottom of the pie plate with the dough.
Fill with chicken mixture. Roll out remaining dough and place on top of the pie. Seal the edges and cut slits to allow steam to escape.
Bake 10 minutes. Lightly cover the pie with foil and bake an additional 15-20 minutes or until golden.
Rest 10 minutes before serving.
Notes
For convenience, the filling may be prepared up to two days ahead before use.
Cover the edges of the crust with foil if it browns too quickly.
Keep leftover chicken pot pie refrigerated in an airtight container for up to 4 days. It can be reheated in the microwave or the oven.
To make ahead, freeze the assembled pie and defrost it in the refrigerator overnight before baking.