03Transfer lamb to work surface. Skim any fat from sauce and discard; season sauce with salt and pepper. Remove meat from bones in bite-size pieces; discard bones. Return meat to sauce in pot. DO AHEAD Can be made 1 day ahead. Cool slightly. Chill uncovered until cold, then cover and keep chilled.
04Bring lamb and sauce to simmer; transfer to large serving bowl. Sprinkle green onions over and serve.