Season chicken with salt and pepper to taste. Heat oil and butter in a very large skillet over medium high heat. Add chicken and saute until golden on one side, 3 to 5 minutes. Turn and repeat on other side. Repeat in batches until all chicken is browned; place on plate or platter and set aside.
In same skillet, saute mushrooms until golden. Stir in garlic and green onion and saute until soft. Sprinkle flour onto mixture and cook, stirring, until mixture is a light color (1 to 2 minutes). Stir in cola beverage, broth, parsley, bay leaf and rosemary and simmer for about 5 minutes, stirring.
Return chicken to skillet, bring to a boil, cover and simmer gently for 25 to 30 minutes or until tender and cooked through (no longer pink inside).
