Rinse chicken and pat dry. Sprinkle with salt and pepper.
Heat 1 T. butter and the oil in large heavy skillet over medium-high heat. Add chicken and cook until well browned on all sides, 15-18 minutes. Using slotted spoon, transfer chicken to plate; pour any fat on plate back into skillet.
Add mushrooms to skillet and cook, stirring occasionally, until light golden, about 3 minutes. Transfer to small plate.
Pour off fat from skillet, leaving thin film of fat and browned bits. Add shallots to skillet and cook until slightly softened, 30-60 seconds. Pour in beef and 1/4 cup cream. Heat to boiling, scraping sides and bottom of skillet with wooden spoon.
Return chicken to skillet, cover, and reduce heat. Simmer, turning pieces once, until chicken is tender, about 20 minutes. Transfer chicken to warm serving platter, cover, and keep warm. (Recipe can be prepared in advance up to this point.).
Skim fat from surface of sauce. Stir in remaining 1/4 cup cream and the mushrooms. Heat to boiling and boil vigorously until sauce is reduce by half. Skim off excess fat if necessary. Stir in mustard, black and cayenne peppers, and any juice from chicken. Taste and adjust seasonings. Remove sauce from heat and whisk in remaining 1 T. butter. Pour sauce over chicken and sprinkle with parsley. Serve hot over buttered noodles.