1. Preheat the oven to 375 degrees F (190 degrees C).

2. Pierce the sweet potato several times with a fork and wrap in aluminum foil. Place on a baking sheet.

3. Roast in the preheated oven until sweet potato is fork-tender, 70 to 90 minutes. Remove from the oven and let cool enough to handle, 5 to 10 minutes.

4. Reduce oven temperature to 350 degrees F (175 degrees C). Lightly grease a 9-inch deep-dish pie plate and place on a rimmed baking sheet to prevent bubbling over.

5. Peel skin off the sweet potato and place flesh into a large bowl. Add butter, milk, salt, pepper, sage, and nutmeg. Beat using an electric mixer until ingredients are combined. Mix in Cheddar cheese gently. Set aside.

6. Heat vegetable oil in a Dutch oven over medium-high heat. Add mushrooms, onion, carrots, celery, and garlic. Sprinkle with salt. Cook until vegetables have softened, 5 to 7 minutes. Add venison, thyme, oregano, garlic powder, onion powder, 1/2 teaspoon salt, pepper, and sage. Stir to combine, breaking up any large pieces of venison. Cook until venison is no longer pink, 5 to 7 minutes.

7. Stir flour into the pot and cook for 1 minute. Pour in white wine and stir to loosen any browned bits from the bottom of the pan. Cook until wine has reduced slightly, 2 to 3 minutes. Stir in broth. Allow mixture to come to a simmer; continue to cook until filling has thickened, 5 to 10 minutes. Stir in peas. Taste and adjust salt and pepper as necessary. Remove from heat and let cool slightly.

8. Pour filling into the prepared pie plate. Top with sweet potato mixture and spread gently across the top, covering most of the filling.

9. Bake in the preheated oven until top is set and filling is bubbling, about 30 minutes. Allow to cool slightly before serving.

Cook's Notes:

To save time, you can boil the sweet potato instead of roasting.

Use any kind of cheese you like for the topping.

For a crispier topping, make sure to use a broiler-safe pan and place the pie under the broiler for a few minutes after baking.