Place a baking sheet upside down in the oven and preheat to 400 degrees F. Beat the eggs, parsley and lemon zest in a small bowl. Pour half of the egg mixture into a medium bowl and stir in the mozzarella. Reserve the remaining egg mixture for brushing on the crust.
Turn another baking sheet upside down; line with parchment paper and brush with olive oil. Unroll the dough on the parchment paper and pat into a 9-by-12-inch rectangle. Spread the mozzarella mixture over one half of the dough, leaving a 1-inch border along the edge. Top with the salami, followed by the pickled vegetables and provolone. Fold the other half of the dough over to cover the filling. Crimp and roll the edges to seal, then pierce the top of the dough in a few places with a knife.
Slide the calzone with the parchment paper onto the hot baking sheet; bake 15 minutes. Remove from the oven and brush with the remaining egg mixture, then continue to bake until the crust is golden, 5 to 10 more minutes. Let rest 5 minutes, then cut into wedges.