Whataburger: Monterey Melt
In the "personal opinion" of our drive-thru operator, the Monterey Melt wins hands down on the messiness front, and we can't disagree. Those peppers and onions are chopped thick enough that one or two dead soldiers will assuredly end up on your lap, especially given that the ranch dressing turns these patties into beef Slip 'N Slides.
Popeyes: Corn on the cob
That corn will not only be seasoned with butter, but also with the delightful cocktail of sweat and grime that comes off your steering wheel as you hold it. In addition, if you have the dexterity to be able to plow a row of corn while driving, why aren't you housing a bucket of Popeyes chicken instead?