For crust, combine flour, sugar, and salt in the bowl of a food processor and pulse until mixed well. Add butter and egg; pulse until combined. Add water to the dough, and pulse until dough begins to form a ball.

Turn dough out onto a floured surface and divide in half. Shape into two flat disks. Wrap, and refrigerate for 30 minutes.

Preheat the oven to 350°. Unwrap 1 disk of dough on a lightly floured surface. Roll to a 16-inch circle, and carefully fit into a 9-inch springform pan, leaving a 1-inch overhang. Refrigerate until ready to use.

For the filling, cook Italian sausage in a large nonstick skillet over medium-high heat, breaking up sausage with a spoon until cooked through. Transfer sausage to a plate and let cool. Whisk ricotta, mozzarella, pepper, and 3 of the eggs in a large bowl. Stir in salami, capicola, and ham.

Add prosciutto slices in the bottom of the prepared dough-lined pan. Spread ricotta mixture over prosciutto. Scatter browned sausage over ricotta mixture, pressing lightly into an even layer. Top with Parmesan.

Unwrap and roll the remaining disk of dough into a 12-inch circle on a lightly floured surface. Place over filling. Trim so that both disks are even with one another, and pinch top and bottom firmly together to seal.

Beat remaining egg and brush over top of pie. Cut 4 vents in the top layer of dough in a circular pattern. Place pie on a rimmed baking sheet, and bake for one hour, or until pie crust is golden brown.

Bake until a thermometer inserted in the center of the pie says 150°F, about 30 more minutes.

Transfer pie to a wire rack, and let cool. Leave pie to set for 30-45 minutes.