Seth, no, not on menus - essentially these are the ‘names’ of the dishes, lists of main ‘components’. 

Easiest way to verify the practice, is to check some menus online. A (not quite) random selection of links below :

 https://www.restaurantcouleursnature.com/

 https://www.thefork.com.au/restaurant/la-tupina-r184/menu

 https://www.leclosduroy.fr/le-restaurant-la-carte-w1.html

The menus in your link are a great illustration of the different uses of de/du etc and au etc in descriptions of food!