1. Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9-inch, deep-dish pie plate.

2. Season venison in a bowl with garlic powder, onion powder, salt, and pepper. Add flour and toss to coat.

3. Heat olive oil in a medium saucepan over medium heat. Add onion and garlic; sauté until soft and translucent, 5 to 7 minutes. Increase the heat to high and add venison. Stir venison to quickly brown, 1 to 2 minutes; don't overcook — it should still be rare inside when taken out of the pan. Transfer venison to a large bowl.

4. Pour red wine and Worcestershire sauce into the pan and bring to a boil while scraping the browned bits of food off the bottom of the pan with a wooden spoon. Cook until liquid has reduced and the pan is almost dry, 10 to 15 minutes. Reduce the heat to low and stir in beef broth.

5. Dissolve cornstarch in water in a small bowl; pour into the pan, whisking constantly. Bring to a simmer and cook until thickened, about 5 minutes.

6. Meanwhile, bring a large pot of lightly salted water to a boil. Add potatoes, carrots, and celery and cook, uncovered, for 2 minutes. Drain in a colander and immediately immerse vegetables into a bowl of ice water for several minutes to stop the cooking process. Drain.

7. Add drained vegetables to venison along with corn and peas; mix until thoroughly combined.

8. Whisk egg and milk together in a small bowl for egg wash and set aside.

9. Line the prepared pie dish with one pastry, trimming the edges if needed. Place venison mixture into pie crust and pour gravy over top. Spread mushrooms over the surface and cover with remaining pastry. Brush with egg wash and cut vents in the top.

10. Bake in the preheated oven until crust is golden brown and filling is bubbling, 45 minutes to 1 hour. If the edges of the crust are getting too dark, cover them with aluminum foil until the center crust has caught up.

11. Let cool for 5 minutes before serving.

Tips

Any quality cut of venison from the rear haunch or loins will work.