Cream butter and sugar in large mixer bowl until light and fluffy. Add eggs and vanilla; beat well. Combine flour, cocoa, baking soda and salt; gradually blend into creamed mixture. Stir in nuts and cherry pieces.
Drop onto ungreased cookie sheet. Bake at 350 degrees until covered with dimples. Do not overbake. (Cookies will be soft; they will puff during baking and flatten upon cooling.)
Cool until set, about 1 minute, remove from cookie sheet; cool completely on wire rack