Adjust oven rack to the upper-middle position and heat oven to 350°F. Combine 1 tablespoon olive oil, garlic, paprika, turmeric, cumin, ginger, and cayenne in a bowl; set aside. In a separate bowl, mash ½ cup chickpeas into a coarse paste with a potato masher.

Pat chicken dry with paper towels and season with ½ teaspoon salt and pepper. Heat the remaining 1 tablespoon olive oil in a 12-inch ovensafe skillet over medium-high heat until just smoking. Cook chicken skin-side down until browned and crisp, 8–10 minutes. Flip chicken and cook for 1 minute; transfer to a plate.

Pour off all but 2 tablespoons of fat from the skillet. Add fennel wedges, cut side down, and sprinkle with ¼ teaspoon salt. Cook until browned, 3–5 minutes per side. Push fennel to the edges and add the spice mixture, lemon zest strips, and cinnamon stick to the center of the skillet. Cook until fragrant, about 30 seconds.

Stir in wine, scraping up browned bits, and cook until nearly evaporated, about 2 minutes. Add chicken broth, whole chickpeas, mashed chickpeas, olives, and apricots, stirring to combine. Nestle chicken thighs into the mixture, skin-side up, keeping skin above the liquid.

Transfer skillet to the oven and roast until the chicken registers 185°F and the fennel is tender, 35–40 minutes. Remove skillet from the oven (using pot holders) and discard lemon zest and cinnamon stick. Adjust seasoning with salt and pepper to taste. Sprinkle parsley over the dish and serve with lemon wedges.