Cheesecake Factory Goes Vegan with the Impossible Burger. You don't think of the Cheesecake Factory as a place to order vegan food, but that's exactly what we're doing as my friend Taylor talks about the different vegan food at Cheesecake Factory and she orders the Impossible Burger. You heard that right, you can now order the Impossible Burger at the Cheesecake Factory. Ordering vegan at the Cheesecake Factory just became much more interesting. The Cheesecake Factory already has some great vegan food, so going vegan at the Cheesecake Factory wasn't hard before, but adding the Impossible Burger to the menu expands the reach of this vegan burger to so many more people. Taylor tries the Impossible Burger for the first time at the Cheesecake Factory and gives us her reaction and also shows you how to order vegan at Cheesecake Factory from the other items on their menu.