Grate the mozzarella through the largest holes of a chesse grater in a bowl. Beat the egg lightly and add to the bowl with the parmesan and flour.
Cut the basil leaves but be sure that the leaves are dry before snipping them with scissors. Mix into the mozzarella mixture with the garlic, pepper and a little salt. Add salt with caution because the parmesan is salty. Toss to combine thoroughly.
Shape the mixture into small balls. Add a little more flour if the mixture is too sloppy. Chill for at least 30 minutes.
Heat oil in a deep saucepan. When the oil is very hot, put the cheese balls. Do not crowd the pan. They will not fry properly. Fish them out with a slotted spoon when they are deep old all over. Put them on kitchen paper to drain. Serve it hot.
