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

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

Heat olive oil in a medium saucepan over medium heat. Add onion and garlic; sauté until soft and translucent, about 5 to 7 minutes.

Increase the heat to high and add venison. Stir venison to quickly brown for 1 to 2 minutes, leaving the center rare. Transfer venison to a large bowl.

Pour red wine and Worcestershire sauce into the pan, bring to a boil, and reduce until almost dry, about 10 to 15 minutes.

Reduce the heat to low and stir in beef broth. Dissolve cornstarch in water, pour into the pan, and simmer until thickened, about 5 minutes.

Bring a large pot of lightly salted water to a boil. Add potatoes, carrots, and celery and cook for 2 minutes. Drain and cool in ice water to stop cooking, then drain again.

Combine drained vegetables, venison, corn, and peas in a bowl. Mix until thoroughly combined.

Prepare an egg wash by whisking egg and milk in a small bowl.

Line the pie dish with one pastry sheet, adding venison mixture and gravy, then top with mushrooms and the second pastry sheet. Brush with egg wash and cut vents.