Pour the olive oil into a medium saucepot fitted with a deep-fry thermometer. Place over medium heat and preheat to 350 degrees F.
Set up a dredging station by placing the flour, egg and breadcrumbs in separate bowls. Working in batches, drop the olives into the flour and roll until evenly coated. Shake off any excess flour and place the olives into the egg. Coat the olives in the egg and lift out, allowing any excess egg to drip off. Roll the olives in the breadcrumbs until evenly coated. Set aside a baking sheet.
Once the oil is hot, carefully add the basil leaves and lemon peels, being aware that the oil may pop. Fry just until crispy, about 30 seconds. Set aside on a paper towel-lined plate. Working in batches, fry the olives until the breadcrumbs are crunchy and the cheese is soft, 1 to 2 minutes on each side. Transfer to a paper towel-lined plate to cool slightly.
Put the olives on a serving platter and crumble the fried basil and lemon zest over top. Sprinkle with freshly cracked pepper.