Heat the olive oil in a large Dutch oven or heavy pot over medium-high. Add the chicken and cook until lightly browned on both sides, 2 to 3 minutes per side. Sprinkle with ½ teaspoon of the paprika, the turmeric and a pinch of the black pepper. Transfer to a plate.
Reduce the heat to medium. Add a little more oil, if needed, then add the onions and mushrooms. Cook, stirring occasionally, until the onions are very soft and lightly caramelized and the mushrooms have released their liquid, 12 to 15 minutes.
Return the chicken and any accumulated juices to the pot. Stir in the remaining paprika, the remaining black pepper, the salt and the date syrup. Pour in enough water to just cover the chicken and bring to a gentle simmer.
Cover, reduce the heat to low and cook until the chicken is tender and the sauce has reduced slightly, 30 to 40 minutes. Taste and adjust the seasoning before serving.
Serve over rice, mashed potatoes or with crusty bread.