Place the yams, tomatoes, chickpeas, and broth in a large pot. Bring to a boil, reduce the heat, cover, and cook, stirring occasionally, for 15 minutes, until the yams are just tender.
Add the remaining ingredients, except for the greens, and mix well.
Place the greens on top of the stew, cover, and steam for 1 minute or so; then stir the leaves into the stew.
Continue to cook, stirring frequently, for 4 minutes. Serve immediately.