In a large Dutch oven or heavy pot, heat the olive oil over medium heat. Add the carrots, celery, and onion and cook, stirring frequently, until softened, about 5-7 minutes. Season with salt and pepper. Add the garlic and tomato paste and cook for 1 minute, stirring consistently.
Meanwhile, prepare the rice: Place the rice in a fine-mesh sieve or bowl and rinse under cold water, swirling and draining repeatedly until the water runs clear. Drain thoroughly and set aside.
Stir in the rinsed rice and toast for 1-2 minutes, stirring constantly. Stir in the turmeric and cayenne pepper.
Pour in the chicken broth and stir in the bay leaf. Bring to a gentle simmer. Taste and adjust seasoning. Continue to simmer until the rice is cooked, about 15-20 minutes, stirring occasionally.
Stir in the shredded chicken and cook for another 2-5 minutes. Taste and adjust seasoning as needed. Remove the bay leaf.
Stir in the chopped parsley and serve with grated parmesan, if desired.
