Hot-dog stands outside the Metropolitan Museum of Art. Photograph by Oliver Morris / Getty

I was halfway through eating a hot dog in Columbus Circle one recent weekend afternoon, when I overheard a tourist say to his kids, “You have to realize you’re in New York.” In case being directly outside Central Park wasn’t enough to remind the children of their whereabouts, a real New Yorker had just barged through the family’s carefully staged photo, leaving them with photographic evidence of the city’s trademark impatience. My hot dog, I thought, paired well with this quintessential New York scene.

I was on a mission, disguised as a jaunt: to walk around the edge of the park and eat a hot dog from every stand I encountered. This initial goal quickly proved impossible, as I was confronted by a veritable throng of carts in Columbus Circle alone. (There are around thirty license-paying concession stands inside the park, but a much larger number operating along the outskirts.) So I resolved, instead, to eat at as many as I comfortably could without lapsing into a frankfurter-induced coma. New York’s hot-dog carts, for all their ubiquity, can feel invisible—more or less indistinguishable vehicles, dishing out what, to the untrained palate, seems like indistinguishable food. I wondered what kinds of surprising variations I might find, and whom I might meet along the way.

Shall I compare that first dog to a summer’s day? It was of reasonable loveliness, and, disconcertingly, on the cooler side of temperate. It cost four dollars, which is a bit steep, as many of the hot dogs around the park will set you back only two or three. Later on, a few blocks north and east, on Fifth Avenue in the sixties, I bought a more competitively priced one from a pair of brothers, originally from Cairo, who were still hung up on a hot-dog-pricing scandal from earlier in the year. In May, a vender near the 9/11 memorial was caught charging customers thirty dollars per dog, and, after being outed in a dramatic NBC New York exposé, was fired by the stand’s owner, who was fined by the city for failing to clearly post his prices.

“I don’t know how we’d sell a hot dog for thirty dollars—even if it’s made out of gold, it’s not going to be thirty dollars,” one of the brothers, Mohammad, told me incredulously. He stood away from the cart to speak with me whilst his sibling, Osama, attended to customers’ orders, yanking frankfurters from their watery container and shifting gyros on the grill. (Many of the stands offering hot dogs today double as Halal carts.) Osama said that he doesn’t eat hot dogs, but Muhammad likes his with ketchup. I ordered mine with ketchup, mustard, and red onion sauce—my preferred combination. “Onions don’t work if you have a girlfriend,” Muhammad said.

My choice of onions was, at least, in keeping with New York hot-dog convention. (The M.I.T.-trained food chemist Alan Geisler, who died in 2009, is credited with having invented the beloved sauce recipe, half a century ago.) Some of my fellow-customers went further astray. On Seventy-fourth Street and Central Park West, at a cart overlooking the Lake, an Italian man ordered his hot dog with ketchup and mayonnaise, and his companion, in a still more dubious choice, took hers plain. A few benches away, a mustachioed man sat down with a classic ketchup-and-mustard in hand and said to a friend, in German-accented English, “Let’s think about life.”

Of the hot dog’s many colorful origin stories, one of my favorites has it that a sports cartoonist named Tad Dorgan coined the name “hot dog” in a cartoon he drew, in 1901, after seeing an entrepreneurial food vender serve up a hot “dachshund” sausage to the crowd at a New York Giants baseball game. A similarly sweet-sounding story says that Anton Feuchtwanger, a sausage vender from Bavaria, invented the hot-dog bun while selling frankfurters at the 1906 St. Louis World Fair. As the legend goes, he initially gave out white gloves with each sausage, so that customers could keep their hands clean whilst eating his sausages, but he eventually substituted milk rolls because people would keep the gloves as souvenirs. According to Dr. Bruce Kraig, the author of the book “Hot Dog: A Global History,” neither story is backed by credible evidence. (The Dorgan cartoon has never even been found.)

What is more certain is that German immigrants began serving frankfurters in New York City in the second half of the nineteenth century, and Nathan’s Famous, the Coney Island hot doggery, founded in 1916, helped to put the city’s franks on the map. The restaurant, which will celebrate its hundredth anniversary next year (presumably with the eating of hot dogs) makes its own all-beef franks, which are sold in their stores and delis but not so much on the street. The majority of hot dogs peddled from carts are Sabrett, the Bronx-made brand that once supplied Nathan’s and still supplies some of the city’s top frank spots. (Tag line: The Frankfurter New Yorkers Relish.)

One hot dog I did not relish, though it may well have been a Sabrett, came from a slightly beleaguered-looking ice-cream and hot-dog stand on Sixty-first Street, just inside the park, where I ordered a frankfurter wrapped inside a cylindrical pretzel bun. The pretzel was stale; the meat a lurid oxblood. Whilst choking it down, I wondered if I might not be better off sitting on a bench, and, like the German man I'd seen, thinking about whether I’d led a meaningful life.

A much better example came on Central Park West in the lower Sixties, where a second Mohammad operated a stand. He told me that he’s from Alexandria and has been in New York for four years. (“Some people are good. Others, not so much,” he said of his customers.) Every winter, when the hot-dog business is sluggish and the park is more amenable to sledding than to lolling and ruminating, Mohammad goes back to Egypt to see his family. I asked him for a hot dog with ketchup and mustard and called my father. It was good—he lives in Europe, and we don’t often get to see each other. The hot dog was good, too—smooth and snappy, the mustard sweet. The key, Mohammad told me, is to ask for the hot dog to be thrown on the grill.

After my filial phone call was finished, I pushed onward and upward along Central Park West. Outside the American Museum of Natural History, I approached a larger stand, where I heard the vender tell a couple that their order had come to forty-nine dollars. At first, I thought that I’d soon be seeing an overzealous NBC New York camera crew rush up to expose the vender’s racket. But moments later a flurry of food came through the window: chicken fingers, four cheeseburgers, fries, and some hot dogs for good measure. The couple brought their grub to a bench, where their eagerly awaiting children sat. I bought a single hot dog from the same cart and sat down on an adjacent bench to marvel at a museum poster featuring a tardigrade—a tiny creature that looks like an inflated vacuum bag. After seven hot dogs, I knew how he felt.