Indeed, in one explanation of their booming popularity, only part of this thrill seems to involve taste, which some say resembles ham. (The 1.5-pound legs are cured with a salt solution.) The real treat comes courtesy of social media sites like YouTube, Flickr, Tumblr and Instagram — being able to post pictures for friends back home, the more primitive the pose the better.

Food review sites like Yelp.com have also spread the word. “I could kiss ’em, caress ’em and sleep with ’em all day and night,” John Giron from Daly City, Calif., wrote of the fare at the Disneyland Turkey Leg Stand. He added, “We’re like a pack of velociraptors gnawing every bit and piece until what’s left are bones and cartilage.”

Boiled down, Disney parks are about selling memories, and a spokeswoman, Angela Bliss, noted that foods like turkey legs play “an integral part in the storytelling.” For instance, at Disney’s Animal Kingdom in Orlando, they have been sold as “dinosaur bones.”

Disney is also in the business of making money, of course, and a jumbo turkey leg sells for up to $11.79.

Still, some executives at Disney’s corporate offices worry that the craze is starting to obscure their efforts to improve overall food offerings and nudge customers toward healthier items. Of the 12 million children’s meals Disney serves annually, for instance, more than 50 percent now come with milk, juice or water instead of soda. Disney has also sharply reduced salt in its children’s meals.