How to Make It
In a very large skillet, heat 2 tablespoons of the oil. Season the chicken with salt and pepper and add it to the skillet in a single layer. Cook over high heat, turning once, until browned but not cooked through, 4 to 5 minutes. Using a slotted spoon, transfer the chicken to a plate. Pour off any fat in the skillet.
Add the remaining 1 tablespoon of oil to the skillet. Add the mushrooms and cook over high heat, stirring occasionally, until browned, 4 to 5 minutes. Add the shallot and cook, stirring, for 2 minutes. Add the wine and cook until reduced to 2 tablespoons, about 4 minutes. Add the stock, cream and mustard and bring to a boil. Cook until the sauce has reduced by half, about 6 minutes.
Return the chicken and any accumulated juices to the skillet and simmer over moderate heat until the chicken is cooked through, 2 to 3 minutes; season with salt and pepper. Stir in the tarragon. Serve with buttered noodles.