In a heavy-bottomed soup pot, over medium heat, add the olive oil and onions. Saute the onions until translucent - about 3-5 minutes.
Next, add the chopped garlic. Stir into the onions and saute for another 2 minutes.
Add the celery, carrots, bay leaves, salt, black pepper, oregano, and thyme. Stir and saute - stirring often - for 7-10 minutes.
Pour in the vegetable stock and stir to combine. Place a lid on the pot and continue to cook for 25-30 minutes. If you carrots are cooked through sooner, you can cut back on the cooking time.
Lastly, reduce the heat to a simmer and add the chopped parsley and cooked rice. Stir into the broth and vegetable mixture.
Since the rice is already cooked, the heat from the broth will warm through the cooled rice quickly. Do not continue to cook or the rice will be over cooked. Serve will still hot.