Line an 8x8" square pan with foil, extending the sides of the foil over the edges of the pan. Mist the foil lightly with cooking spray.
Dip the chocolate graham crackers quickly, working one at a time into the chocolate milk. Line them up side by side in the pan, breaking some of the crackers to fit. You should have one even layer. Set aside briefly.
In a large bowl with an electric mixer, cream together the cream cheese, Nutella, and vanilla extract on medium speed until combined and fluffy, about 1 minute. Using a rubber spatula, fold in the whipped topping until fully incorporated. Spoon 1/4 of the Nutella mixture evenly over the graham crackers.
Repeat layers twice more, for a total of three (3) layers. Spoon and spread the remaining Nutella mixture over the top. Cover with plastic wrap and refrigerate until firm, at least 4-6 hours. Just before cutting into squares, garnish with chocolate curls or miniature chocolate chips and whole hazelnuts.