Cream butter and sugar until light and fluffy. Beat in egg and vanilla. Combine flour, cocoa, baking powder and salt. Fold dry ingredients into creamed mixture by hand to moisten dry ingredients and avoid dusting; then mix just until blended.
Form dough into two 10 to 11-inch long logs on sheets of parchment paper. Position each log in the center of the parchment paper. Pour half of the chopped pistachios in a line parallel with each log of dough; roll logs in nuts to thoroughly cover the outside of each log. Wrap each log in parchment paper and chill for 2 or 3 hours.
Preheat oven to 325°F.
Slice the log into ¼-inch slices and put on an ungreased cookie sheet about 1-inch apart.
Bake 10-12 minutes.