Preheat oven to 375° with rack in center. Prepare crust; In the bowl of a food processor, combine flour, sugar, baking powder, and salt. Pulse to combine.
Add butter; pulse until mixture resembles cornmeal. With processor running, add eggs and process until dough comes together and forms a ball, about 1 minute.
Transfer to a lightly floured work surface, and knead until smooth, 3 to 5 minutes.
Prepare filling; In a large bowl, stir together ricotta, eggs, Parmesan, mozzarella, prosciutto, parsley, and pepper; set aside.
Divide dough into 2 pieces, one slightly larger than the other. Roll larger piece into a 12-inch circle; gently transfer to a 9-inch glass pie dish.
Place filling in pie plate and spread evenly; set aside.
Roll remaining dough into a 9-by-9-inch square; cut into 1/2-inch wide strips. Using strips, form a lattice pattern over filling. Trim bottom crust, leaving a 1/2-inch overhang. Crimp edges to seal. Brush with egg, and bake until filling is firm, 40 to 45 minutes. Let cool completely before serving.