I'm not sure if the current offerings include more substantial food items (like they used to have rotisserie chicken), but it seems there is always this option:
Picnic in the Park is available to anyone via a grab-and-go area in the Beastly Bazaar in Discovery Island. Guests may purchase a picnic for a group of 2, 4, or 6 people and select a non-alcoholic beverage, a choice of sandwich, chips, and dessert. The sandwich choices include Turkey Focaccia; Ham and Salami on Ciabatta; Tuna on Pita; Vegetarian Wrap; and Chicken Caesar Wrap.
I believe you get a reusable shopping bag to carry your food in and keep as a souvenir.