Arrange 36 wafers on bottom and up side of 9-inch pie plate. Drizzle with 2 Tbsp. coffee.
Beat cream cheese in large bowl with mixer until creamy. Gradually beat in milk. Add dry pudding mix; beat 1 min. Gently stir in 2 cups cool whip.
Layer half each of the pudding mixture and grated chocolate in crust; cover with remaining wafers. Drizzle with remaining coffee. Repeat layers of pudding and chocolate. Top with remaining cool whip. Refrigerate 3 hours.