What is a Basque Cheesecake? A Basque Cheesecake is a baked cheesecake with few ingredients and direct method. The uniqueness of the Basque Cheesecake is its simplicity. The list of ingredients for the Basque cheesecake is short and simple. It is a baked cake like the New York Cheesecake, but one of the characteristics that sets it apart is that it does not have a cookie base or crust. Unlike other cheesecakes, it does not contain butter among its ingredients and it is not presented with the typical jam or fruit topping that characterizes the most classic cheesecakes.