Whip the heavy cream with the confectioners’ sugar until it forms stiff peaks. Add the Chobani and whisk to combine.
In a 9-in square pan add 4 rows of cookies, 4 cookies to a row (16 cookies total). Evenly spread ⅓ of the Chobani mixture over the cookies. Top with another 4 rows of cookies and half of the remaining Chobani mixture. Finish with the remaining Chobani and the remaining Chobani mixture.
Cover the baking dish with plastic wrap and refrigerate overnight.
Before serving, use a grater or vegetable peeler to grate or shave chocolate over the cake.