Melt The Butter In A Skillet Over Medium Heat. Season The Chicken On Both Sides With Pepper; Cook The Chicken Breasts In The Butter Until No Longer Pink In The Center And The Juices Run Clear, 6 To 7 Minutes Each Side. An Instant-Read Thermometer Inserted Into The Center Should Read At Least 165 Degrees F (74 Degrees C). Remove The Breasts From The Pan And Set Aside. Stir Together The Onion, Parsley, Applesauce, Wine, Mustard, And Half-And-Half In The Pan; Bring The Mixture To A Boil And Cook About 5 Minutes. Return The Chicken To The Pan; Add The Walnuts. Allow To Cook Until The Chicken Is Warm, 3 To 5 Minutes.