Season both sides of the chicken pieces with salt and pepper. Heat the oil in a large, heavy-bottomed deep skillet or Dutch oven over medium-high heat until shimmering.
Add the chicken pieces, skin side down, in a single layer (work in batches if necessary). Cook them until golden brown, about 5 minutes. Flip the chicken pieces over and brown the other side for about 3 more minutes. If the pan becomes too hot, reduce the heat to medium. Transfer the chicken to a plate and set it aside.
Reduce the heat to medium. Add the onion slices and cook, stirring occasionally, until golden brown, for about 5 minutes. If the pan becomes too dry, add 1-2 tablespoons of water.
Add the minced garlic, ginger, and spice mix. Cook, stirring, until fragrant, about 30 seconds.
Stir in the broth, scraping the bottom of the pan with a wooden spoon to loosen any browned bits.
Add the chicken back in, skin side up. Nestle the lemon slices and olives around the chicken pieces. Bring the mixture back to a steady simmer.
Reduce the heat to medium-low, cover, and simmer until the chicken is cooked through, for 20-30 minutes.
Garnish with cilantro and serve.
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Notes
Depending on the size of your pan, you might need to brown the chicken pieces in two batches. I use a fairly small Dutch oven to make this recipe, so I brown four chicken pieces first and then the remaining ones.You can keep the leftovers in the fridge, in an airtight container, for up to 4 days. Reheat them gently, covered (to prevent splatters), in the microwave at 50% power. You can also freeze the leftovers for up to three months.