Preheat the oven to 375°F.
Remove the pie crust from the refrigerator and let it sit at room temperature for 10–15 minutes so it’s easier to work with. Fit the crust into a 9-inch pie dish, pressing it gently into the bottom and sides.
Use a fork to poke holes all over the bottom of the crust, spacing them about 1 inch apart. Bake for 6-8 minutes, just until the crust is set but not browned. Remove from the oven and set aside.
In a large bowl, whisk together the eggs and egg yolk until well combined and slightly frothy. In a separate bowl, stir the ricotta until smooth and loosened.
Add the ricotta to the egg mixture and gently fold until just combined and smooth.
Gently fold in the prosciutto, mortadella, buffalo mozzarella, Parmesan, and parsley, until evenly distributed.
Pour the filling into the pre-baked crust and smooth the top.
Bake uncovered for 40–45 minutes, until the edges are fully set and the center has a slight jiggle. If the crust edges begin to brown too quickly, loosely cover just the edges with foil halfway through baking.
Remove from the oven and let the pie cool for 10 minutes before slicing. The filling will continue to set as it rests.