Cook rice and barley ahead of time according to package instructions. Set aside.
Heat oil over medium high heat in a large stock pot. Add garlic, onion, carrots, and celery and cook until slightly soft and the onion is translucent, about 5 minutes.
Stir in the flour and thyme and stir constantly for about 3 minutes. Pour in the chicken stock slowly and whisk until all the lumps are dissolved. Bring to a boil
Add chicken and mushrooms and simmer for about 15 minutes. Add the barley and wild rice and half and half and heat to a boil for 6 or 7 minutes until heated through.
Serve warm with fresh parsley on top.