Heat the olive oil in a large pot over medium heat. Add the onion, garlic, carrots, and celery, and cook until the vegetables are tender, about 5-7 minutes.
Add the rice, chicken broth, and water to the pot. Bring to a boil, then reduce the heat to a simmer.
Simmer the soup for 20-25 minutes, or until the rice is tender.
Add the diced turkey and frozen peas to the pot, and simmer for an additional 5 minutes, or until the peas are tender.
Season the soup with salt and pepper to taste.
Serve the soup hot, garnished with chopped fresh herbs if desired.