Preheat the oven to 375°F. Lightly spray a 10- inch tart pan with cooking spray. If using a premade crust, allow the pie crust to sit on the counter for 15 minutes before you attempt to unroll. After warming to room temperature, fit the pie crust into the tart pan.
In a small mixing bowl, whisk together 1 1/4 cups of heavy cream, 5 eggs, 1 tablespoon chopped parsley, 1 teaspoon onion powder, 1/2 teaspoon of garlic powder and salt, 1/4 teaspoon of dry mustard and a pinch of nutmeg. Add black pepper to your taste.
Arrange the diced ham over the bottom of the pie crust, and sprinkle the Parmesan cheese on top. Sprinkle 1 cup of Swiss cheese over the Parmesan.
Spread the chopped spinach over the cheese. Pour the filling evenly over the spinach layer. Sprinkle the remaining shredded Swiss cheese on top.
Place into the preheated oven and bake for 30 minutes. Allow the quiche to stand on the counter for at least 20 minutes before cutting.