Using a mixer and mixing bowl, beat the butter until fluffy, about 2 minutes Add the sugar and mix together until smooth.
In a small bowl, stir the egg with the vanilla and add to the butter mixture, blending well.
Sift together the flour, cocoa, baking soda, and salt. Add to the butter mixture in three stages, blending well after each addition. Add the peanut butter and blend well.
Divide the dough into thirds. Place each piece on a large rectangle of wax paper and roll each cylinder about 7 inches long and 1 inch thick.
Place chopped peanuts in a shallow pan. Roll each cookie dough log in peanuts to coat the outside of the log. Wrap the logs in wax paper, wrap again in plastic wrap or place in a resealable bag. Chill at least 2 hours. (The dough can be frozen at this point. Defrost overnight in the refrigerator before using.).
Preheat oven to 350 degrees. Line a cookie sheet with parchment paper. Cut each cylinder into 1/2 inch thick slices. Place on the cookie sheet, with 2 inches between cookies.
Bake for 10 minutes or until firm. Remove the cookie sheets from the over and transfer cookies to cooling racks.