Heat a large heavy-bottomed pot over medium heat. Season the chicken lightly with salt and pepper on both sides. Add olive oil to the pot.
Carefully place the chicken in the pot in a single layer, and cook for 3-4 minutes per side until chicken has become golden and fragrant. Remove the chicken from the pot and set aside on a large plate.
Add the onion and garlic to the pot, cooking in the rendered chicken fat. Scrape up all the brown bits from the bottom of the pot. Cook for 2-3 minutes until the onion is soft. Add the turmeric, cinnamon, paprika and cumin to the pot. By adding the spices now, you are basically toasting them in the hot oil. This releases their aromas and flavors more intensely than if you added them to the simmering liquid.
Return the chicken to the pot, along with all of the largely cut veggies and the chicken broth.
Bring the stew to a simmer, then place the lid on top (ajar) and continue to cook for about 35 minutes. Add additional salt to taste.
Meanwhile, make the couscous according to the package directions, and set aside until the stew is ready, when the sweet potatoes are fork tender and the chicken is very soft.
Serve in large shallow bowls, with plenty of broth. Sprinkle the chopped parsley on top.