I am very sensitive and have never had any issues here! They use Udi's buns (at least I think so) and list their fries and sweet potato fries as gluten-free. The fries come in GIANT quantities, the small can feed multiple people. The burgers are very good. They have a topping bar so all burgers come plain and dry, beyond any specialty toppings that come on a specific sandwich. There aren't many cheap/quick GF burger options in Georgetown, so Burger University takes the cake in my opinion.