Heat oven to 350°F. In small bowl, place sugar.
In large bowl, break up cookie dough. Stir or knead in cocoa until well blended. Shape dough into 64 (1-inch) balls. On ungreased cookie sheets, place balls 2 inches apart. Press each flat, with smooth-bottomed glass dipped in sugar.
Bake 6 to 9 minutes or until cookies are set. Cool 1 minute; remove from cookie sheets to cooling racks. Cool completely, about 20 minutes.
In medium bowl, beat filling ingredients with electric mixer on medium speed until light and fluffy. Spread about 2 heaping teaspoons filling between bottoms of pairs of cooled cookies.