1. In a small bowl, stir together mayonnaise and capers. Season to taste and set aside.
2. In a medium bowl, whisk together flour, cornstarch and baking powder. Add sparkling water and whisk until smooth. Refrigerate until ready to use.
3. Heat vegetable oil in a large heavy bottomed pot to 300F.
4. Add parsley leaves in batches, frying until crispy, about 5 seconds. Remove with a slotted spoon to a paper towel-lined plate to drain. Sprinkle with salt while still warm. Set aside.
5. Increase heat to medium high and heat oil to 350F.
6. Dip vegetables in batter, one at a time, allowing excess batter to drain off. Carefully place dipped vegetables in oil and cook until golden brown. Remove from oil with a slotted spoon and place on a paper towel-lined plate to drain. Sprinkle with salt and pepper while still warm. Repeat dipping and frying with remaining vegetable pieces.
7. Roll the bocconcini in breadcrumbs and add to oil, being careful not to overcrowd the pot. Cook until golden brown and melting on the inside. Remove with a slotted spoon to a paper towel-lined plate to drain. Repeat with remaining bocconcini if necessary.