Preheat oven to 425°. Stir together pickled vegetables, next 4 ingredients, and 1 Tbsp. olive oil.
Place dough on a lightly floured surface. Cut dough into 4 equal pieces. Roll each piece into a 7-inch circle.
Place 2 dough circles on a lightly greased baking sheet. Spoon vegetable mixture on top of circles, mounding mixture on dough and leaving a 1-inch border. Moisten edges of dough with water, and top with remaining 2 dough circles. Press and crimp edges to seal.
Cut small slits in tops of dough to allow steam to escape. Brush with remaining 1 Tbsp. olive oil, and sprinkle with Parmesan cheese.
Bake at 425° for 20 to 24 minutes or until golden brown.