Heat a large deep saute pan over medium heat. Add the butter and olive oil.
Brown the chicken parts on all sides until a deep golden brown. Remove from pan.
Add the onion, mushrooms and garlic. Saute until onion is slightly tender. Add chicken stock and scrape up all the burny bits from the bottom of the pan (deglazing). Add the wine, salt, pepper, rosemary, carrots and chicken back to the pan.
Bring to boil, reduce heat, cover and simmer for 30 minutes.
Remove cover and increase heat to medium. Reduce liquid by 25-50% depending on how much juice you like (I reduced by 50%).
Stir in the cream and heat through. Stir in the cheese. Correct seasonings at this point.
Serve with crusty bread and a nice green salad.