In a large pot over medium heat, warm the olive oil. Add the onion, carrot, and ½ teaspoon salt. Cook for 5 minutes or until softened and lightly caramelized, stirring occasionally.
Add the tomato paste and cook for 1 minute, stirring often. Add the spices for another 30 seconds, stirring constantly. Quickly add the water (so the spices don’t burn), rice, chicken, and remaining 1 teaspoon salt.
Bring to a boil over high heat, then give the soup a stir, making sure no rice is stuck to the bottom. Simmer uncovered over low/medium-low heat for 15 minutes, or until the chicken and rice are cooked through, stirring halfway through.
Remove the chicken and shred it up. Return it to the soup along with your greens and stir to wilt the greens.
Serve topped with a dollop of yogurt, fresh herbs, pomegranate seeds (if using), and some black pepper.