In a pot large enough for the chicken, heat the olive oil on medium heat. Add the onion, and sauté for 5 minutes until it begins to soften.
Add the chicken to the pot, the pour in the water. The water won’t cover the chicken.
Add the garlic, cinnamon, cardamom and ginger. Add salt and pepper to taste.
Simmer the chicken, covered, for 1 1/2 hours, turning the chicken over after 45 minutes. Keep an eye on the pot to adjust the heat as needed to keep the simmer going without bringing it to a boil.
After the 90 minutes cooking time, remove the chicken to a large platter, keeping the cooking liquid in the pot. The chicken should be very tender. After it has cooled, remove and discard the skin. Pull the chicken off the bones, and break into pieces, serving size and smaller.
Meanwhile, bring the cooking liquid to a boil, and add the lemon juice. Stir in the orzo, and cook for 10 minutes, stirring occasionally. Add up to a cup of additional water if the cooking liquid gets absorbed prior to the 10 minutes.
Add the chicken pieces into the pot with the orzo. Simmer the chicken with the orzo for 3 to 5 minutes until most of the liquid has been absorbed and the orzo is tender. Stir in the 1/3 cup feta cheese.
Plate the chicken orzo mixture, and pass additional feta cheese for topping at the table. Enjoy!