Preheat your oven to 375ºF.
Heat the olive oil in a large skillet over medium-high heat. Once hot, add the ground turkey and brown one side for 3-4 minutes before breaking apart and adding the onion. Mix everything together and cook until the turkey is fully cooked and the onions have softened, about 3-4 minutes.
Turn off the heat and stir in the garlic and seasonings. Cook for about 1 minute until the garlic is fragrant.
Add the can of soup and frozen vegetables and stir everything together. This should cool the mixture, making it thick enough to add the mashed potato crust without chilling. (If your filling is too slack, you can chill in the refrigerator or transfer to another baking dish to cool faster before adding the potatoes.)
For the crust, microwave the mashed potatoes for 3-4 minutes before adding in an even layer on top of the ground turkey filling. Top with the cheese and a drizzle of olive oil.
Bake for 50-60 minutes until the crust is golden brown. Top with freshly chopped parsley and grated parmesan. Let the pie rest for 15-20 minutes before serving.