Step 1Cut each riblet in half. Put the meat and garbanzos in a medium pot; add 2 1/4 cups water. Bring to a boil, reduce the heat to low and simmer until tender, about 30 to 40 minutes, removing any scum that comes to the top. Add the salt and cook 5 minutes more. Remove the meat and beans from the water. Strain the cooking liquid and skim excess fat from the surface. Reserve 1 cup and discard the rest.
Step 2Wash, drain and chop the spinach. Put the spinach in a large pot with the reserved 1 cup cooking liquid, butter, vinegar and pekmez. Bring to a boil; reduce the heat to simmer and cook, covered, until the spinach is soft, 8 to 10 minutes.
Step 3Stir in the meat and garbanzos and cook over medium heat until warmed through. Serve with rice.