Heat oven to 350 degrees F.
Work together cookie dough and cocoa powder with wooden spoon in bowl until well blended and smooth. (If dough becomes too soft to work with, refrigerate to firm, about 10 minutes.) Drop dough by slightly rounded teaspoonfuls, 2 inches apart, onto large ungreased baking sheets (you should have about 40 cookies). For each cookie, dampen bottom of small glass with water; dip in sugar; press down on cookie to flatten to about 2 inches in diameter.
Bake in 350 degree F oven 8 to 10 minutes or until puffed and slightly crisp around edge. Remove sheet to wire rack and cool cookies 1 minute. Remove cookies from sheet to rack and cool completely.
Beat together heavy cream, confectioners sugar and vanilla in small bowl until stiff peaks form. Stir together milk and instant coffee in glass measure to dissolve coffee. Gradually beat coffee mixture into cream cheese in small bowl until smooth and well blended. Fold in half of whipped cream.
Coarsely break about one-third of cookies into bottom of 11 x 7-inch baking dish. Spread half of cream cheese mixture evenly over top of cookies. Layer with another third of broken cookies and remaining cream cheese mixture. Top with remaining broken cookies and whipped cream. Sprinkle with grated chocolate, if desired.
Cover tightly. Refrigerate at least 8 hours or up to 24 hours for cookies to soften before serving. Makes 12 servings.