Drain the olives. Remove any filling from the centers, if necessary, and place the olives in a bowl. Drizzle lightly with olive oil and toss to coat.

Cut the mozzarella into pieces just small enough to fit into the hole of the olives. Stuff each of the olives with a piece of the cheese. Sprinkle 2 tablespoons of flour over the olives and toss to coat.

Heat the oil in a small pot over medium heat for about 5 minutes, to about 350°F.

Break the eggs into a shallow bowl and beat lightly.

Combine the cornmeal and 1/3 cup flour in a mixing bowl. Season lightly with pepper and toss to combine. Dip the floured olives in the beaten egg, letting any excess drip back into the bowl. Coat the olives all over with the cornmeal and flour mixture and place them on a tray or large plate.

Fry the olives in a couple of batches until golden brown, about 3 minutes, but not so long that the cheese oozes out from the center of the olives.

Drain the fried olives on paper towels to absorb any excess oil. Serve as soon as possible–the fresher the better!