Place a large Dutch oven or cast iron braiser over medium heat. Add the bacon and cook until almost crisp, about 4 minutes.
Add the squash, turnips, and carrots to the pot. Depending on how much fat was released from the bacon, you may need to add a little olive oil. You need about 1 tablespoon of fat/oil in the pot when you add the veggies. Cook the veggies, stirring occasionally, for 5 minutes.
Add the chicken and shallots. Stirring often, cook an additional 5 minutes.
Add the garlic and herbs, stirring until fragrant, about 1 minute.
Add the flour and stir to coat everything in the pot. Cook for a minute.
Slowly add in the chicken stock while stirring to incorporate. Scrape up an brown bits from the bottom of the pan with a wooden spoon as you stir. Stir in the apple cider vinegar and maple syrup. Add the ½ cup of extra stock if the mixture seems too thick - you want it to be the consistency of a thick stew.
Bring the everything in the pot to a low boil over medium-high heat. Reduce heat to a simmer, and cook for 5 minutes to thicken. Remove pot from heat and allow to the mixture to cool for 10 minutes.
Place a rack in the lower ? of your oven. While the pot pie filling is cooling, preheat your oven to 450 degrees F.
Grease two 10’’ pie pans with cooking spray. Evenly divide the pot pie mixture into each. At this point, you can either bake the pies once you add the crust on top OR you can freeze the filling for later use.
While the oven is heating and after you have filled your pie pans, roll out your pie crust on a floured surface. Add it to the top of the pie pan and crimp as desired. Brush the entire top of the pie lightly with the egg + water mixture. Cut two small slits in the top of the pie and place it on a large baking sheet.
Place the baking sheet in the lower third of your oven and bake for 10 minutes. Reduce heat to 425 degrees F and continue baking for an additional 20 minutes until the top of the crust is golden brown.
Remove the pie from the oven and let it sit for 10 minutes before serving. Leftover pie will keep in the refrigerator for up to 3 days.
If you want to make this for the freezer, freeze the pot pie filling in the pie dish and the crust separately. When ready to bake, thaw the pot pie filling in the fridge overnight. Top with the pie crust when you are ready to bake and proceed with baking instructions from above. Frozen pot pie filling will keep up to 6 months in the freezer.