In a large bowl, cream 1 cup butter and confectioners' sugar until light and fluffy. Add flour and vanilla; mix well. Cover and refrigerate for 1 hour.
Shape 1/4 cupfuls of dough into 1/2-in. thick logs. Cut logs into 2-1/2-in. pieces; place on ungreased baking sheets. Bake at 350° for 12-14 minutes or until lightly browned. Remove to wire racks to cool.
In a heavy saucepan or microwave, melt chocolate and remaining butter; stir until smooth. Dip one end of each cookie into chocolate, then dip into nuts; place on waxed paper until chocolate is set.