Rinse chicken, pat dry and sprinkle both sides with the flour. Saute' chicken in hot butter in a large skillet until golden on each side (about 15 minutes). Add consumme and simmer (covered) approximately 35 minutes.
Saute the mushrooms in olive oil in a seperate pan for 20 minutes or until tender. Reserve mushrooms.
Remove the chicken breasts to a heatproof serving dish and add the sauteed mushrooms. Stir in sour cream, salt and pepper to the consomme sauce and strain the sauce over the chicken.
Sprinkle the parmesan cheese over the top of the chicken. Place under the broiler for about 3 minutes or until golden brown.