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More than 1,000 times a minute, someone bites into what has been described as a wet envelope of cat food—and keeps eating.

Jack in the Box is known to most of the country for its hamburgers and bigheaded mascot. But for many of its devotees, the magic of the fast-food chain lies in its interpretation of a taco.

A tortilla wrapped around a beef filling that is dunked in a fryer and topped with American cheese, lettuce and hot sauce, the taco appeared on the menu in the 1950s after the first Jack in the Box opened in San Diego. As the chain spread beyond California, the taco has followed it —with good reason. Jack in the Box now sells more tacos than any other item on its menu thanks to a legion of fans who swear by the greasy vessels even as they sometimes struggle to understand their appeal.

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The first time Heather Johnson tasted a Jack in the Box taco, she was at a drive-through in Cincinnati when she noticed you could get two for 99 cents, so she added them to her burger order.

She took two bites, threw the rest on the passenger seat and kept driving. “It was stale, greasy, spicy, crunchy, saucy and just plain strange,” said Ms. Johnson, a 43-year-old director of operations at an advertising agency in Cincinnati and author of a blog called the Food Hussy. “Who puts a slice of American cheese in a taco?”

Two minutes later, she picked the taco off the seat and finished it. Then she ate the other one.

“I was like, ‘I must have more. This is vile and amazing,’” she said.

Mike Primavera believes when it comes to Jack in the Box tacos, there are two kinds of people: those who think they’re disgusting and those who agree they’re disgusting but are powerless to resist them.

He first tried one about 10 years ago when he stopped at a Jack in the Box on his way home from a bar. “I remember pulling it out of the sleeve, and even though I was drunk I was like, ‘I shouldn’t eat this.’ But damn it was good,” said Mr. Primavera, an equipment manager for a general contractor in Seattle. “I’ve been addicted to them ever since.”

Mr. Primavera, who made the cat food comment on Twitter, said the secret to the tacos’ goodness may be the juxtaposition of the “soggy, nasty middle” and the “rim of crunchiness on the outside” that comes from deep-frying the tortilla with the beef filling already inside. One key, he said: “You can’t look at it too long before you eat it. You just kind of have to get it outside of the sleeve and into your mouth.”

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Every Jack in the Box taco is born at one of three plants in Texas and Kansas, where tortillas made from stone-ground white corn are cut, cooked and filled with the beef mixture. They are shrink-wrapped and frozen and eventually shipped to stores to be fried, topped and served in taco-sized bags. The company sells 554 million tacos a year, or about 1,055 a minute.

That is about the same number of Big Macs McDonald’s says it sold in the U.S. in 2007, the last time it says it tracked that figure.

This article originally ran in The Wall Street Journal.