BEAT cream cheese in large bowl with electric mixer on medium speed until creamy. Gradually add milk, beating well after each addition. Add dry pudding mix; beat on low speed 1 min. or until well blended.
SPRINKLE cut sides of ladyfingers with coffee; place 1/3 of the ladyfingers on bottom of 9-inch square dish. Top with layers of 1/2 each of the pudding mixture and whipped topping; sprinkle with 1/3 of the grated chocolate. Repeat all layers. Top with remaining ladyfingers and grated chocolate.
REFRIGERATE 3 hours or until ready to serve. Store leftover dessert in refrigerator.