To a large bowl, mix together 150 grams flour with sugar and salt.
Cut the cold, unsalted butter into small chunks and add to the flour mixture. Using a pastry cutter, cut the butter into the flour mixture until all of the butter is moistened by the flour and forms a thick paste.
Add the remaining 175 grams of flour and use the pastry cutter to distribute the flour until the mixture looks crumbly. Pour the chilled sourdough discard on top of the flour/butter mixture and stir to combine. Use your hands to form the dough into a ball. If the dough is too crumbly, add ice-cold water, one Tablespoon at a time, until it comes together.
Cut the ball in half and form two balls of dough. Wrap the balls in plastic wrap, press down on them to form a disc shape and stick in the refrigerator to chill. Chill the dough for 20 minutes in the refrigerator.
While the dough chills, prepare the filling by heating a large skillet over medium heat. Melt the butter, then add the chopped celery and onion, cooking for 3–4 minutes until softened. Stir in the minced garlic and cook for another minute. Add the salt, pepper, celery seed, garlic powder, and bouillon paste, mixing well to coat the vegetables with the seasonings.
Whisk the sourdough discard and milk together in a small bowl until smooth. Pour the mixture into the pan with the sautéed vegetables, whisking until it begins to thicken. Stir in the chicken broth and cook until the filling thickens. Add the shredded chicken and frozen vegetables, stirring until evenly combined. Remove from the heat and set aside.
Position the oven rack in the middle to the lower half of the oven and preheat to 425ºF.
Remove the chilled pie dough from the refrigerator and lightly flour a pastry mat or countertop. Roll out the first disc of dough into a circle just over 10 inches wide. Fold the dough into quarters, place it in a pie plate, then unfold and gently fit it to the dish, leaving the edges hanging over. Roll out the second disc of dough to the same size or slightly larger, for the top crust and set aside.
Prick a few holes in the bottom of the pie crust using a fork. Spoon the cooled chicken pot pie filling into the prepared bottom crust, then lay the second crust over the top. Trim the excess dough with kitchen scissors, then fold the top crust edges under the bottom crust, pressing gently to seal the pie all the way around. Crimp the sealed edges of the pie, adding any decorative touches to the crust as desired.
Whisk a medium egg with a splash of water, then brush the egg wash evenly over the top crust. Cut two or more slits in the crust to let steam escape during baking. Bake at 425ºF for 30–35 minutes, until the crust is golden brown and the filling is bubbling.
Let cool for a few minutes and then slice and enjoy!
