In a large pot or Dutch oven, heat the olive oil over medium heat.
Add the diced carrots, celery, and onion, sautéing until softened, about 5-7 minutes.
Add minced garlic and cook for another minute until fragrant.
Stir in the flour and cook for 1-2 minutes to create a blonde roux.
Gradually whisk in the chicken stock and water, ensuring the roux is fully incorporated.
Add the dry rice blend, seasoning packet, black pepper, oregano, and bay leaf.
Bring the mixture to a slow boil, then reduce heat to low and simmer for 20-25 minutes, or until the rice is tender.
Stir in the shredded chicken and 2 cups of milk.
Simmer on low for an additional 5-10 minutes to heat through and allow the soup to thicken.
Remove the bay leaf and serve warm.