Season chicken with salt and pepper. Poach in lightly salted water or bake at 375°F (190°C) for about 25 minutes, until internal temperature reaches 165°F (74°C). Rest for 5 minutes, then shred with two forks.
Preheat oven to 375°F (190°C). Melt butter in an oven safe skillet over medium heat. Cook onion, celery, and carrots for 5 to 6 minutes until onion is translucent. Add garlic and cook 30 seconds until fragrant. Add cauliflower and cook 3 to 4 minutes until softened.
Pour in chicken broth and bring to a simmer, scraping up browned bits. Sprinkle xanthan gum while whisking constantly. Reduce heat to low and stir in heavy cream and 4 ounces cream cheese, whisking until smooth. Add poultry seasoning, salt, and pepper. Simmer 4 to 5 minutes until thickened.
Fold shredded chicken and frozen peas into the thickened sauce. Remove from heat and let cool for 5 minutes. If using a separate pie dish, transfer filling now.
In a microwave safe bowl, combine mozzarella and remaining 1 ounce cream cheese. Microwave in 30 second bursts, stirring between, until melted and smooth. Add almond flour, egg, and baking powder, and stir quickly with a spatula until dough forms. Let cool 1 to 2 minutes if too warm.
Place dough between two sheets of parchment paper. Roll out until slightly larger than the top of your skillet or pie dish, about 1/8 inch thick. Peel off top parchment and use bottom sheet to flip and lay dough over the filling.
Trim excess dough and press edges to seal. Cut 3 or 4 small slits in the top. Brush evenly with beaten egg wash. Bake for 20 to 25 minutes until golden brown and filling is bubbling.
Rest the pie for 10 minutes before serving. This allows the filling to set so it won't run when cut. Slice into 6 portions and serve warm.