Pat the chicken dry and season it on all sides with the salt and black pepper. Heat the olive oil in a Dutch oven or other heavy, lidded pot over medium-high heat. Brown the chicken, skin-side down first, in batches if needed, for 4 to 5 minutes per side. Transfer the browned chicken to a plate.
Lower the heat to medium. Add the onion to the same pot and cook, stirring occasionally, until softened and lightly golden, about 7 minutes. Add the garlic, ginger, cumin, turmeric, paprika, cinnamon, and optional cayenne. Stir for 30 seconds, just until fragrant.
Pour in the chicken broth and honey, scraping up any browned bits from the bottom of the pot. Return the chicken and any juices on the plate to the pot, arranging the pieces skin-side up. The liquid should come about one-third of the way up the chicken; add a small splash of water if needed.
Bring the liquid to a gentle simmer. Cover, reduce the heat to low, and cook for 25 minutes. Turn the chicken pieces over, add the dried apricots and green olives around the chicken, then cover and simmer until the chicken is tender and reaches 165°F (74°C) in the thickest part without touching bone, about 15 to 20 minutes more.
Transfer the chicken to a warm serving dish. If the sauce is thinner than you prefer, simmer it uncovered for 3 to 5 minutes. Stir in the lemon juice, then taste and adjust the salt and pepper as needed.
Spoon the apricots, olives, and sauce over the chicken. Sprinkle with cilantro, parsley, and optional toasted almonds. Serve hot with lemon wedges, couscous, crusty bread, or rice to catch the sauce.