Season chicken thighs with salt and pepper on one side. Heat olive oil in large, deep skillet over medium-high heat. Place chicken, seasoned side down, in skillet. Sprinkle salt and pepper on unseasoned side, and cook until browned on both sides, about 12 minutes total. Transfer to large bowl and set aside.
Carefully drain all but one tablespoon of oil from the skillet.
Return skillet to medium high heat and add onion slices. Cook, stirring frequently, for about 8 minutes. (If the chicken has left a lot of fond on the bottom of the skillet, add 1 tablespoon of the chicken broth to the onions and scrape the bottom of the skillet, then continue sautéing.)
Add the carrot pieces and cook for an additional two minutes, stirring from time to time.
Add garlic and cook for about 30 seconds, stirring well. Add paprika, ginger, turmeric, cinnamon, and cayenne and cook for one more minute, stirring constantly but carefully.
Add the chicken broth to the skillet and scrape the bottom of the pan as you stir it in. Return the chicken pieces and any juices that have collected in the bowl to the skillet.
Add the lemon slices to the skillet and bring whole mixture to a boil.
Lower the heat to simmer, cover the skillet and cook for about 30 minutes, turning chicken pieces over from time to time.
Sprinkle chicken and vegetables with half of the parsley. Serve, garnishing each dish with a cooked lemon slice or two and a bit of the remaining parsley.