1. For the crust: Place coconut oil in freezer for 15 minutes.
2. While coconut oil chills, in the bowl of a food processor, combine flour, xanthan gum, salt, and sugar. Pulse a few times to combine.
3. Cut chilled coconut oil into chunks.
4. Place coconut oil, vinegar, and eggs into food processor. Pulse 20 times to get the mixture started.
5. Turn processor on low and process until dough starts to come together. It should be sandy but sticks together when squeezed in your hand.
6. Turn dough out onto a lightly floured surface. Squeeze dough into a cohesive ball. You should still see pea size and smaller chunks of coconut oil.
7. Slightly flatten ball into a disc. This will make it easier to roll out.
8. Wrap in parchment and then wrap tightly with plastic wrap.
9. Refrigerate for at least 1 hour or up to overnight.
10. While dough is chilling, prepare the chicken pie filling.
11. For the filling: Peel and dice carrots. Peel onion. Chop onion and celery. Crack egg into bowl and stir in milk. Cut cream cheese into cubes and set aside. Set aside.
12. Place carrots and celery in a large pot with chicken and cover with water.
13. Add in bay leaf and bring water to a boil. Reduce temperature down to simmer.
14. Simmer chicken and veggies for 15 minutes. When done, drain water and set aside.
15. When cool enough to handle, shred chicken or cut into cubes.
16. Meanwhile, preheat oven to 350F.
17. Heat oil in a pan over medium-high heat.
18. Add onions, garlic, thyme, rosemary, salt, and pepper, and cook until onions are translucent.
19. Add flour and stir and cook until all flour is absorbed.
20. Add in chicken broth and stir, scraping bottom of pan.
21. Cook for 3-5 minutes until thickened. Remove from heat and add in cream cheese. Stir until melted and smooth.
22. Taste and adjust seasonings to your preference.
23. Take pie crust out of fridge and allow it to warm up for 15 minutes.
24. Cut disc in half and place one half on a lightly floured surface. Wrap up remaining half until ready to use.
25. Using your hands and/or generously floured rolling pin, press pie crust into a circle large enough to cover bottom of pie plate.
26. Take your time, mending cracks as you go, trying to keep it as circular as possible.
27. Very carefully, roll crust up onto rolling pin and use it to help you place crust into pie plate.
28. Use your hands to carefully work the dough up the side of the pie plate, forming the full crust.
29. Turn remaining dough onto a floured surface.
30. Using your hands and/or a generously floured rolling pin, roll crust out to a 1/4 inch thick and about 12 inches wide. Again, take your time, mending cracks and trying to keep it as circular as possible.
31. Place chicken, veggies, and peas into pie plate and pour sauce over.
32. Very carefully roll crust up onto rolling pin and use it to help you place crust on top of pie.
33. Seal the edges by pinching between your fingers to create a fluted crust or by using a fork to press the edges closed.
34. Using a sharp knife, cut off any excess crust hanging over. Cut a couple slits in the top to allow steam to escape.
35. With a pastry brush, paint top crust with egg wash.
36. Bake for 35-40 minutes until crust is golden brown and filling is bubbling.
37. Check, starting at 25 minutes, to make sure edges of crust aren't browning too quickly. Place aluminum foil strips or a pie crust shield around edges to prevent burning.
38. Remove pie and allow to sit for 15-20 minutes before slicing. The filling will thicken as it cools. Enjoy!