Preheat the oven to 400 degrees F. Lightly coat 4 mini pie dishes (for mini pies) or 1, 9-inch regular pie dish with nonstick spray.
In a large, deep nonstick skillet, heat the oil over medium heat. When the pan is hot, add the shallot, parsley, thyme, and sage and cook until almost soft and fragrant, 2 to 3 minutes.
Add the celery and cook until the vegetables are soft, 3 to 5 minutes.
Add the frozen mixed vegetables, 2 cups broth, the bouillon, salt, and black pepper, and bring to a boil. Simmer for about 5 minutes, stirring frequently, until the flavors meld.
Add the turkey.
Meanwhile, combine the remaining 1⁄4 cup broth with the cornstarch in a bowl and mix well to dissolve. Add to the skillet and cook over medium-low heat, stirring until thickened, 4 to 6 minutes.
Remove from the heat and transfer to the prepared pie plate(s). Place the plate(s) on a sheet pan to catch any drips.
Roll out the pie crust to be slightly larger than your dish (if cooking mini pies, cut out 4 rounds slightly larger than the pie plates). Place the crust over the turkey filling. Crimp the edges or fold over the edge of the pie plate. Poke holes in the top of the dough with a thin, sharp knife.
Brush the crust with the egg and immediately bake on the sheet pan for 25 to 35 minutes, or until the crust is golden and the filling is hot and bubbly.
TO FREEZE AND SERVE LATER: Freeze the pot pies without the egg wash: let the filling cool completely in the pie dish before adding the crust. Top with crust, then flash freeze for 1 to 2 hours, then cover each tightly with plastic wrap or transfer carefully to zip-top plastic bags. To cook, remove from the freezer, brush the pie crusts with egg wash, and place on a baking sheet. Bake at 400 degrees F for 50 to 55 minutes (for mini pies; 1 single pie will need a little longer), or until golden and heated through in the center.
TO STORE: Refrigerate pot pie in an airtight storage container for up to 4 days.
TO REHEAT: Rewarm leftovers in a pie dish in the oven at 350 degrees F.
TO FREEZE: Store turkey pot pie in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.