Roll into balls about the size of a tangerine and place one cube of cheese into the rice ball. Reform balls firmly to hold shape.
Place flour, egg and breadcrumbs into 3 separate bowls.
Dip each ball in flour, shaking off excess and reform if needed. Dip in egg, letting excess drip off, then dredge in bread crumbs, reforming and transfer to a sheet of wax paper. Repeat with remaining balls.
Meanwhile heat 2 inches of oil in a 4- to 5-quart heavy pot until thermometer registers 350-360 degrees F. Working in batches of 4-6 balls, lower rice balls into oil with a slotted spoon and fry, turning occasionally, until golden brown, 2 to 3 minutes per batch. Transfer with slotted spoon to paper towels to drain. Return oil to 350-360°F between batches.