Season the chicken. Pat the chicken dry with a paper towel, then season generously on all sides with 2 tsp kosher salt and ½ tsp black pepper.
Brown the chicken. Heat 3 Tbsp of olive oil in a large pan over medium-high heat. When hot, add chicken thighs skin-side down, working in batches as needed, and cook until browned on both sides, about 10-12 minutes. Transfer to a large plate, then reduce the heat to medium.
Cook the onion. Add sliced onion, then season with ½ tsp kosher salt. Cook, stirring occasionally, until softened, about 4-5 minutes. Add chopped garlic, 1 tsp paprika, 1 tsp ground cumin, ½ tsp ginger, ½ tsp turmeric, ¼ tsp ground cinnamon, and ¼ tsp cayenne pepper. Cook, stirring occasionally, for 1-2 minutes.
Simmer. Pour in 2 cups (475ml) low-sodium chicken broth, then use a spatula to scrape up any browned bits from the bottom of the pan. Stir in 1 cup (140g) halved green olives and the chopped preserved lemon. Return the chicken to the pan, along with any juices, then bring up to a boil. Lower the heat to a simmer, then cover the pan and cook until the chicken is fully cooked through, about 20-25 minutes. The chicken is safe to eat when it reaches an internal temperature of 165°F (74°C).
Garnish, then serve! Taste the sauce, adjust the seasoning as needed, then transfer the chicken pieces to a large platter. Spoon the sauce on top, then sprinkle with chopped fresh cilantro and additional lemon rounds or wedges for serving. Enjoy immediately with couscous!