Cut chilled cheese in 6 equal wedges. In a shallow bowl, beat egg. On a sheet of wax paper, mix Italian bread crumbs and crushed dry green tea leaves.
Dip each cheese wedge in egg and turn to coat. Roll cheese in crumb mixture to coat. (If preparing ahead, cover and refrigerate now until ready to cook.)
In a heavy saucepan, heat about 2 inches of olive oil to high (until a 1-inch bread cube turns golden brown on all sides). Fry cheese until golden. Drain on paper towels.