Combine yogurt, garlic, cumin, paprika, ginger, lime zest, salt, coriander, and turmeric in a large ziplock plastic freezer bag; remove and reserve 1/4 cup of the yogurt mixture. Add chicken to remaining yogurt mixture in bag; seal bag and rub to coat. Chill for 8 to 24 hours, turning occasionally.
Preheat oven to 400°F with top rack 6 inches from broiler. Place chicken on a greased wire rack fitted on a foil-lined baking sheet. Bake on top rack until a meat thermometer inserted into thickest portion registers 130°F, 15 to 17 minutes. Turn broiler on.
Broil chicken until thermometer registers 165°F, 6 to 7 minutes, basting with reserved yogurt mixture every 2 minutes. (There should be char after each basting interval.) Remove from oven and let rest for 5 to 10 minutes. Cut chicken into large chunks. Sprinkle with cilantro and serve with lime wedges.