Place chicken breasts between two pieces of plastic on a cutting board and pound out to an even thickness ¾ - 1-inch thick.
Season them well with salt and pepper.
Place the flour or cornstarch in a wide shallow bowl. Dredge the chicken breasts coating them lightly on each side.
Heat a large frying pan over medium heat and melt the butter.
Add the chicken and cook about 7 - 8 minutes. Turn them over and cook another 5 - 7 minutes or so - until internal temperature on a meat thermometer (into the center of the breast) registers 165 - 174 degrees F.
Remove the chicken breasts to a platter and cover with foil.
Add 1 + ½ tablespoons green onions to the skillet and cook for 1 minute.
Add the heavy whipping cream and whisk the wine and mustard into it.
Bring to a simmer while whisking and cook 2 - 3 minutes.
Ladle over the chicken and garnish with the remaining green onions to serve.