Preheat the oven to 375°F (190°C) and line a 9-inch round cake pan or springform pan with parchment paper, leaving an overhang for easy removal.

Thaw the puff pastry sheets completely, unroll one sheet on a clean surface, and press it into the bottom and up the sides of the prepared pan. Prick the bottom lightly with a fork.

Cut the prosciutto, capicola, and salami into 1/4-inch dice and place in a large mixing bowl.

In a separate bowl, whisk together the eggs, ricotta, shredded mozzarella, grated Pecorino Romano, chopped parsley, salt, pepper, and red pepper flakes until pale and well combined.

Gently fold the diced meats into the egg and cheese mixture until evenly distributed without overmixing the eggs.

Pour the filling into the pastry-lined pan, spreading it evenly to reach the edge of the crust. Wipe away any excess filling from the rim.

Unroll the second puff pastry sheet and place it over the filling. Tuck and press the edges together to seal the pie.

Brush the top crust with the egg wash (beaten egg and water) and bake for 45 to 50 minutes, until the crust is golden brown and the filling is set (center should reach 160–165°F/71–74°C).

Allow the pizza rustica to cool in the pan for 10–15 minutes before using the parchment overhang or releasing the springform to transfer to a cutting board. Slice and serve warm or at room temperature.