Sauté the base. Heat 1 to 2 tablespoons olive oil in a large pot over medium heat. Add onion, carrots, and celery with a pinch of salt. Cook 5 to 7 minutes until softened.
Stir in garlic and cook 30 seconds until fragrant.
Add broth and seasonings. Pour in the chicken broth. Add bay leaf and dried oregano. Bring to a gentle boil.
Cook the chicken. If using raw chicken, add it to the pot now.
Reduce to a simmer, cover, and cook 12 to 18 minutes, depending on thickness, until cooked through. Remove chicken to a plate and shred with two forks.
Simmer the rice. Stir the rice into the pot. Keep at a gentle simmer and cook 12 to 15 minutes for white rice, stirring occasionally to prevent sticking.
If using brown rice, cook it separately and add at the end.
Return the chicken. Add the shredded chicken back to the pot. Simmer 3 to 5 minutes to warm through and blend flavors.
Add lemon and herbs. Turn off the heat. Stir in lemon zest and lemon juice, then taste.
Adjust with more lemon, salt, or pepper as needed. Fold in chopped dill or parsley. If adding spinach or peas, stir them in now to wilt.
Finish and serve. Remove the bay leaf.
Ladle into bowls and finish with a drizzle of olive oil, extra herbs, and fresh black pepper.