In a large pot or Dutch oven, heat olive oil (or butter) over medium heat. Once hot, add the chopped onions, carrots, and celery. Stir occasionally until the vegetables are softened and slightly golden, which should take around 5-7 minutes.

Push the vegetables to one side of the pot, then add the minced garlic and sauté it for about 1 minute until fragrant. Place the chicken breasts in the pot and cook until lightly browned on both sides, about 3-4 minutes per side.

Pour in the chicken broth, water, and barley. Add the bay leaf and thyme for extra flavor. Bring the mixture to a gentle boil.

Lower the heat to a simmer, cover the pot, and let it cook for about 30 minutes. Stir occasionally and check the barley’s tenderness. You want it to be soft but still have a bit of chewiness.

Once the chicken is cooked through, remove it from the pot and shred it using two forks. Return the shredded chicken to the soup and stir well.

Pour in the heavy cream, and stir to combine. Let the soup simmer for an additional 5-7 minutes, allowing the flavors to meld and the soup to thicken slightly.

Taste the soup, and season with salt and pepper as needed. Remove the bay leaf before serving. Ladle the creamy chicken barley soup into bowls and garnish with freshly chopped parsley if desired.