Simmer rice, 3 scallions, turkey carcass (break into pieces if necessary), half of ginger, and water in a 6-to 8-quart heavy pot, covered, stirring occasionally, until soup has a creamy, porridge-like consistency, 50 minutes to 1 hour.
Meanwhile, thinly slice remaining 3 scallions and julienne remaining ginger.
Discard turkey bones. Serve jook sprinkled with scallions and ginger.
