Chop the onions finely. Clean and quarter the mushrooms. Remove the moisture from the chicken pieces with paper towels. Heat up a large, Dutch oven over a medium flame. Melt 2 Tbl of butter in the pan, searing the chicken until all sides are golden-brown. Remove the chicken from the pan and de-grease the pan. Melt another 2 Tbl of fresh butter in the pan, throw in the onions and sweat them down. Pour in the wine and scape the bottom of the pan. Return the chicken to the pan. Season to taste with salt and pepper. Bring the contents of the pan to the boil - slowly - then cover and cut the heat to a simmer.
Periodically, rearrange the chicken pieces. Braise for 25 minutes, then add the mushrooms. Simmer 15 minutes more. Remove the chicken from the pan. Reduce the pan's liquid over a medium flame. When somewhat reduced, throw in the heavy cream and reduce further, until the sauce coats the back of a spoon. Ladle the sauce over the chicken. Serve.