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Step 1
Heat the olive oil in a large pot over medium heat. Meanwhile, dice the onion (and mince the garlic if using fresh rather than pre-minced). Add the onion and garlic to the hot oil and saute until tender (5 min).
Step 2
If using fresh carrots and celery, clean and slice them while the onions are sauteing. Add them to the pot and cook for about 5 minutes more.
Step 3
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 simmer for one hour.
Step 4
Near the end of the hour, begin to make the creamy milk mixture. In a small pot, melt 2 Tbsp of butter over medium heat. When it is fully melted, whisk in 2 Tbsp of all-purpose flour. Cook and stir the butter and flour mixture for two minutes. Whisk in the milk and allow it to come up to a simmer, whisking occasionally to keep it from scorching on the bottom. Once it reaches a simmer, it will have thickened slightly.
Step 5
Carefully remove the chicken pieces from the soup and shred or dice with a knife and fork. Rinse and chop the parsley. Add the parsley and the thickened milk mixture to the soup. Season with salt to taste. I used about 2 tsp of salt, but start with a little and add more as needed. I also added a touch more pepper at this point. Serve hot!