PLACE hazelnut spread and instant coffee in medium bowl. Gradually whisk in brewed coffee, whisking until smooth.
BEAT cream cheese in large bowl with electric mixer on medium speed until fluffy. Add milk, pudding mix and vanilla. Beat until smooth and thickened, about 2 minutes. Fold in whipped topping.
SPREAD about 1/2 cup cream cheese mixture in bottom of 8- or 9-inch square baking dish. Top evenly with 16 ladyfingers. Drizzle evenly with 1/3 of coffee mixture, spreading with back of spoon to coat ladyfingers. Top with 1 1/3 cups cream cheese mixture. Repeat layers twice, using all remaining ladyfingers, coffee mixture and cream cheese mixture. Sift cocoa powder evenly over top. Chill several hours or overnight before serving.