In a 4- to 6-quart pan over medium heat, stir pine nuts and 1/4 cup green onions in oil until nuts begin to brown and onions are limp, about 5 minutes.
Stir in rice, chicken broth, grape leaves and reserved 1/4 cup brine, lemon juice, raisins, and pepper. Bring to a boil, then reduce heat to low, cover, and simmer until liquid is absorbed and rice is tender to bite, 30 to 35 minutes.
Fluff rice mixture with a fork; stir in parsley, dill, and remaining 1/4 cup green onions. Mound salad on a platter and garnish with lemon quarters if desired. Serve warm or at room temperature.