Shake Shack tells you the answer themselves - their own FAQ says they use pure soybean oil in all their fryers, which covers every chicken item, the 'Shroom Burger, the crinkle cut fries and the crispy onions. They publish no ingredient statements at all, so additives are unknown, and independent testing found detectable plasticizers in all three Shake Shack items sampled.
Shake Shack answers the oil question themselves, in their own FAQ, verbatim: "We use cholesterol-free, pure soybean oil in all our fryers to cook our chicken products, 'Shrooms, fries and crispy onions." Read live on shakeshack.com/faq this run. That is every fried thing they sell - all the chicken, the 'Shroom Burger, the crinkle cut fries that come with nearly every order, and the crispy onions on the ShackBurger. The beef patties are griddled and they do not say in what, and they publish nothing about the potato bun or ShackSauce, so those are genuinely unknown rather than clean. They publish no ingredient statements at all - the only document behind "Nutrition & Allergen Info" is a 16-page nutrition and allergen grid with no ingredient column - so additives could not be answered honestly and were left blank rather than guessed. Plastics: plasticlist.org tested three Shake Shack items in Palo Alto and all three came back with detectable plasticizers.