Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low, cover, and simmer until tender, about 20 minutes. Drain; steam dry potatoes in pot for 1 to 2 minutes. Add half-and-half, 2 tablespoons butter, salt, and black pepper; mash. Set aside.

Preheat the oven to 400 degrees F (200 degrees C).

Cook elk meat, Italian seasoning, salt, and black pepper in a skillet over medium-high heat until crumbly and no longer pink, about 5 minutes. Transfer to a 9-inch pie plate or baking dish; return skillet to the stove over medium heat.

Add onion, parsnip, and garlic powder to the skillet; season with salt and black pepper. Cook until parsnip has softened, about 10 minutes. Stir in mixed vegetables; cook 5 minutes, then add to pie plate on top of elk. Top vegetable mixture with mashed potatoes; brush 1 tablespoon melted butter on top.