Chop the onions finely. Clean and quarter the mushrooms. Remove the excess moisture from the chicken pieces with paper towels. Heat up a Dutch oven over a medium flame. Sear the chicken in oil until golden-brown. Remove the chicken, and degrease the pot. Melt 1 Tbl of butter in the pot, sprinkle in the flour and whisk the roux constantly - until it becomes lightly brown. Add 1 more Tbl of butter, throw in the onions, and sweat them down. Pour in the wine, whisk to combine and scape the bottom of the pan. Return the chicken to the pan, season with salt, pepper and ground cayenne pepper. Bring the contents of the pan to the boil cover and cut the heat to a simmer.
Periodically, rearrange the chicken pieces. After 20 minutes, throw the mushrooms into the pot. Braise the chicken for 15 more minutes. When the chicken is tender, remove it from the pan. Reduce the pan's liquid over a medium flame. When somewhat reduced, throw in the heavy cream and nutmeg. Reduce the sauce, until it barely coats the back of a spoon. Return the chicken to the pot. Drench it in sauce. Serve over rice.