Preheat oven to 200°F.
Note: to clarify butter: Put the butter in a stainless steel bowl in a 200 degree oven. After 1 hour, skim off the crust on top. Put the bowl in the refrigerator. When the butter has re solidified, turn it out of the bowl. Scrape off and discard the white solid layer of milk solids (this is what burns during frying). Wrap and refrigerate the yellow layer of clarified butter until needed. One pound of butter yields about 14 oz. of clarified butter.
Mix the flour with the 1 teaspoon each of salt and of pepper.
Dredge the chicken in the seasoned flour and shake off the excess.
Heat the clarified butter in a skillet and add the chicken and sauté over medium heat for 5 minutes. Turn the chicken and sauté for 3-5 more minutes or until just done.
Remove from the skillet and keep warm in the oven.
Discard any butter left in the pan.
Add the shallots, vermouth, and brandy to the pan; turn the heat to high and reduce the liquid to 3 tablespoons while stirring to scrape up any browned bits.
Whisk in the mustard. Add the salt, pepper, and cream and cook over medium-high heat for 2-3 minutes, stirring occasionally, until mixture is the consistency of a light gravy.
Transfer the chicken from the oven to dinner plates, mask with the sauce, dust with the parsley and serve at once.