Add 2 ½ cups gluten-free all-purpose flour and ½ teaspoon salt to food processor bowl. Pulse until just combined.
Add 2 4-ounce sticks unsalted butter (cubed) to food processor bowl. Pulse just until mixture is crumbly, with pea-sized chunks of butter remaining.
Drizzle 1 teaspoon apple cider vinegar over crumbly mixture.
Turn food processor on at low speed. While processing mixture, slowly pour ⅓ cup cold water into food processor through feed tube. Once dough is well-mixed but still lumpy, stop food processor. Dough should be fully combined, with no dry flour remaining, and shapeless but not smooth. It should stick to itself when pinched. Be careful not to add too much water or over-mix dough.
Lightly flour flat work surface, then transfer dough mixture to floured surface. Shape dough into single ball, then divide ball into 2 equal halves. Be careful not to overwork dough.
Form each half into one flat disc, then wrap discs in plastic wrap. Place wrapped discs in refrigerator and chill at least 30 minutes, up to 48 hours. See Notes below to freeze dough instead.
When ready to use dough, remove dough discs from refrigerator and let sit at room temperature 10 to 20 minutes or until slightly softened.
Spread parchment paper out on flat work surface, then lightly flour parchment paper. Unwrap dough discs and place on floured parchment paper.
Use rolling pin to carefully roll dough out into two evenly-thick discs, large enough to fit in 9-inch pie plate and cover edges. Lightly flour rolling pin as needed if dough sticks. If dough begins to crack right away, let dough sit at room temperature 5 to 10 minutes more. Edges of dough will likely crack even if dough is soft enough to roll - simply pinch and patch tears as needed.
Carefully lift one rolled dough disc off parchment paper. Center disc over pie plate and gently press dough onto bottom of plate, into corners, and up edges of plate as needed, forming bottom pot pie crust.
Gently poke tines of fork into bottom pie crust, creating small vent holes across entire crust. Be careful not to make too many vent holes, or to make vent holes too large. Set pie dish and remaining rolled dough disc aside.
For the Pot Pie Filling
Preheat oven to 400° Fahrenheit. Position oven racks so that pie plate will sit in center of oven.
Place large saucepan on stovetop over medium-high heat. Add 2 cups low-sodium chicken broth, 2 small red potatoes, 1 medium stalk celery, 1 medium carrot (finely chopped), ½ cup diced yellow onion, and ½ cup frozen peas to saucepan. Stir to incorporate, then bring liquid to boil.
Once broth begins to boil, immediately reduce heat to low. Simmer broth and vegetables 10 minutes, or until potatoes are just fork-tender.
When potatoes are tender, add 2 cups chopped roasted chicken. Stir to incorporate, then simmer mixture 5 to 10 minutes more, until chicken and peas are warmed through.
While vegetables simmer, heat small saucepan on stovetop over medium-high heat. Add 4 tablespoons unsalted butter to saucepan and let butter melt, swirling and tilting saucepan occasionally to distribute butter across entire surface.
Once butter is melted, sprinkle 4 tablespoons gluten-free all-purpose flour into saucepan. Vigorously whisk flour into butter until fully combined and paste-like. Cook mixture, stirring occasionally, until roux is golden in color.
Once roux is golden, remove saucepan from heat. Let cool slightly, then slowly add ½ cup milk (at room temperature), whisking constantly until ingredients are fully incorporated. Return saucepan to heat and reduce heat to low.
Add 1 tablespoon dried sage, 1 tablespoon dried thyme, 1 pinch nutmeg, salt (to taste), and freshly ground black pepper (to taste). Whisk to incorporate aromatics, then simmer mixture, whisking constantly, until thickened.
Once mixture has thickened, add mixture into large saucepan with chicken and vegetables. Whisk well until both mixtures are fully combined into one, then pour filling into pie plate, filling bottom pie crust.
Carefully lift remaining dough disc off of parchment paper and center over pie plate. Gently place dough onto pie plate, covering filling and edges of plate completely.
Carefully tuck edge of top crust behind edge of bottom crust, then gently press crusts' edges together with tines of fork, making sure to seal entire perimeter of pie.
Make small vent holes or slits in center of top crust with fork or knife.
To Bake and Serve the Gluten-Free Chicken Pot Pie
Place prepared pot pie on center rack in preheated oven. Bake pot pie 35 minutes, then begin checking doneness. Continue baking as needed, checking pot pie regularly, until filling is hot and bubbly and crust is golden.
Once pot pie is baked as desired, carefully remove pot pie from oven and set aside. Let pot pie rest 5 minutes, then serve as desired.
Recipe Notes
Chicken Broth: Not all varieties of chicken broth are gluten free! Some brands will use flavorings and preservatives that contain gluten, so be sure to double check yours before using it.
Sage: It's important that you use dried sage and NOT fresh or ground sage. Fresh or ground sage will overpower the rest of the dish and may turn the filling green.
Make it Dairy Free: Use a plant-based butter. Replace the milk with almond milk.
Make it Vegetarian: Replace the chicken with 2 cups of preferred meat alternative or vegetables of choice. Use a gluten-free vegetable broth instead of chicken broth.
Make it Vegan: Use a plant-based butter and replace the milk with almond milk. Use vegetable broth instead of chicken broth, and replace the chicken with a meat alternative or extra vegetables.
Freezer Options
To Freeze Dough: Wrap dough discs in plastic wrap, then place wrapped discs in freezer for 30 minutes. After 30 minutes, transfer discs to sealable freezer bags. Freeze wrapped dough discs in bags up to 3 months. Defrost in refrigerator overnight before using.
To Freeze Prepared Pot Pie: Prepare the pot pie as instructed, letting the filling cool in the pie plate before covering it with the top crust. After placing the top crust, wrap the entire pie first with plastic wrap and then with aluminum foil. Place the wrapped pot pie in the freezer and keep frozen up to 2 months. When ready to bake, defrost the pie completely in the fridge, then follow the baking instructions above. I like to use an aluminum pie plate for this so my nicer pie plates aren't stuck in the freezer for a month or two.