Gather all of your ingredients.

Heat the olive oil in a large pot over medium heat.

Dice the onion and mince the garlic. Add the onion and garlic to the hot oil and sauté until tender, about 5 minutes.

If using fresh carrots and celery, clean and slice them while the onions are sautéing, then add to the pot and cook for about 5 minutes more.

Add the chicken breast (whole), bay leaf, oregano, thyme, cracked pepper, dry rice, and 6 cups of water to the pot. Do not add salt yet.

Bring the pot up to a boil over medium-high heat, then reduce the heat to low and let it simmer for one hour.

Near the end of the hour, make the creamy milk mixture. In a small pot, melt 2 Tbsp of butter over medium heat.

When the butter is fully melted, whisk in 2 Tbsp of all-purpose flour. Cook and stir for two minutes.

Whisk in the milk and allow it to come up to a simmer, whisking occasionally to prevent scorching.

Once it reaches a simmer and thickens slightly, remove it from the heat.

In the pot, carefully shred the chicken with two forks.

Rinse and chop the parsley.

Add the parsley and the thickened milk mixture to the soup. Season with salt to taste.