Sprinkle about half a teaspoon each of Cajun seasoning, white pepper, oregano, garlic powder, and allspice on the chicken pieces.
Heat 1-2 tablespoons of olive oil in a large pot over medium heat. Add the seasoned chicken and cook until golden brown on both sides, about 3-4 minutes per side. Remove the chicken from the pot and set aside on a plate.
Chop the onion, celery, and bell peppers. Grate the carrot.
In the same pot, add the chopped onion, celery, bell peppers, and grated carrot. (Add a little more oil if necessary.) Sauté the vegetables for about 5 minutes, stirring occasionally, until they are softened.
Return the seared chicken to the pot, then add the potato chunks. Pour in 3 cups of water.
Allow everything to cook together on medium heat for 15-20 minutes, or until the potatoes are tender and the chicken is fully cooked.
Carefully remove the chicken pieces from the pot and shred them with two forks. Set aside.
In a bowl, whisk together 1 tablespoon of flour, 1 egg, and 3 tablespoons of plain yogurt until smooth. Scoop about ½ cup of hot broth from the pot and slowly whisk it into the yogurt mixture to help prevent lumps.
Slowly pour the thickened mixture into the pot, stirring well as you add it.
Add the shredded chicken back into the pot. Taste and add more spices or a pinch of salt if needed.
Let the soup simmer on low heat for another 5 minutes to blend the flavors.
Your Turkish-style chicken soup is ready to serve! Garnish with fresh coriander if you like. Enjoy!