Mix the rice, tuna, egg, garlic, tomato paste, Parmesan cheese, salt, and basil. Refrigerate until the whole mixture is cold all the way through.
Take one tablespoon of the rice and tuna mixture and flatten it with the back of a fork or your hands. Place one of the mozzarella cubes and place it on the top. Then form another patty to cover over the cheese. Seal sides together.
Dust with lightly with flour, then dip into the beaten egg and immediately coat with bread crumbs. Repeat until all patties are formed.
In hot oil, fry about 3 tuna cakes at a time. Flipping once, and cook until golden brown. Place on paper towels to drain.