In a small bowl, mix together the cumin, paprika, coriander, oregano, garlic powder, turmeric and 1½ tsp of salt.
In a large bowl, toss the chicken with the vinegar and add half the spice blend, rubbing it all over the chicken. Let stand for at least 20 minutes or refrigerate for up to 8 hours.
In a large Dutch oven or other heavy saucepan with a tight-fitting lid over medium heat, warm 2 tsp of the olive oil. Add the chicken and cook until golden brown on the bottom (3-4 minutes).
Flip and cook until golden brown on the other side (3-4 minutes longer); adjust heat as necessary to prevent the spices from burning. Transfer the chicken to a plate.
Add the remaining ¼ cup of the olive oil, then add the onion, garlic, and bell pepper, season generously with salt and pepper, and cook, scraping up any browned bits from the bottom of the pan, until very soft, about 10 minutes.
Add the tomato and cook until softened, about 2 minutes. Add the remaining spice blend and cook until fragrant, about 1 minute.
Add the rice and several large pinches of salt and stir to coat the rice. Add the stock, increase the heat to medium-high, and bring to a boil. Lower the heat to medium-low, return the chicken to the pot, and cover with the lid.
Cook until the rice is tender and absorbs the liquid, about 20 minutes. Turn off the heat, add the peas and let stand for 5 minutes. Uncover, fluff the rice, and stir in the peas as well as the olives.
Season with more salt and pepper if necessary. Sprinkle with cilantro and serve, passing hot sauce at the table.
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