1. Prepare the Sourdough Discard Crust: In a large bowl, whisk together 1 1/2 cups flour and 1/2 teaspoon salt. Add the cold, cubed butter and cut it into the flour mixture using a pastry blender, your fingertips, or a food processor until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining. Stir in the sourdough discard. Gradually add the ice water, 1 tablespoon at a time, mixing until the dough just comes together. Be careful not to overmix. Form the dough into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes.

2. Saute the Aromatics: While the dough chills, heat the olive oil in a large oven-safe skillet or Dutch oven over medium heat. Add the chopped onion, carrots, and celery. Cook, stirring occasionally, for 5-7 minutes, until the vegetables begin to soften. Stir in the dried thyme and the remaining 1/2 teaspoon salt and black pepper.

3. Make the Roux: Push the vegetables to one side of the skillet. Add the 1/4 cup butter to the empty side and let it melt. Once melted, sprinkle in the 1/4 cup flour over the butter and stir constantly for 1-2 minutes to create a roux. This will thicken your pot pie filling.

4. Build the Creamy Filling: Gradually whisk in the chicken broth into the roux, stirring until smooth. Then, slowly whisk in the milk until the mixture is well combined and begins to thicken. Bring the mixture to a gentle simmer, stirring frequently, and cook for 2-3 minutes until it’s a creamy, thick consistency.

5. Combine Filling Ingredients: Remove the skillet from the heat. Stir in the shredded or diced cooked turkey, frozen peas, and frozen corn. Taste the filling and adjust seasonings if necessary.

6. Assemble the Pot Pie: Preheat your oven to 400 F (200 C). On a lightly floured surface, roll out the chilled sourdough discard dough into a circle slightly larger than your skillet or pie dish. Carefully place the rolled-out dough over the turkey filling in the skillet, trimming any excess dough and crimping the edges to seal. Cut a few slits in the top of the crust to allow steam to escape.

7. Bake to Golden Perfection: Brush the top of the crust with the beaten egg wash. Place the skillet on a baking sheet (to catch any potential drips) and bake for 35-40 minutes, or until the crust is golden brown and the filling is bubbly. If the crust starts to brown too quickly, you can loosely tent it with aluminum foil.

8. Rest and Serve: Let the pot pie rest for 10-15 minutes before serving. This allows the filling to set and prevents it from being too runny when you cut into it. Serve warm and enjoy!