In the 1930s, Harry J. Hoenselaar was just another ham salesman in Detroit trying to find an edge.

He spent his days handing out samples of honey-glazed ham and teaching drugstore clerks how to slice it for sandwiches. Although he was a master at knifing ham from the bone, he knew there had to be a better way.

His family, which still runs the Honey Baked Ham Co. he founded in 1957, says the answer came to him in a dream. With a tire jack, a pie tin, a washing machine motor and a knife, he fashioned the world’s first spiral ham slicer — a contraption that would become one of the world’s great ham innovations.

If an aged country ham is like jazz, funky and improvised, a spiral-cut is the pop music of the ham world — sweet, approachable and easy to eat. It’s a rare critic who won’t grab a slice of the tender, pale pink meat given the chance.

The spiral ham’s natural habitat is the buffet table, at holidays like Easter and life events like graduations, where the pre-cut meat slides effortlessly onto a plate. As spiral-ham marketers like to say: It virtually serves itself!

FOR THOSE who need a primer on ham: a fresh ham is an uncooked primal cut of pork from the rear leg of the animal. Take that cut, rub it in salt and maybe some spice, smoke it over wood and hang it several months to age and you’ve got country ham.

Raw ham soaked in or injected with brine, spice, sugar and curing agents and perhaps smoked a little creates city ham, preferred for the spiral machine.

Making a city ham is a speedy process. “There’s a pig on Monday, and it’s in the store on Friday,” said Sam Edwards III, of the Edwards Virginia Smokehouse family. His bone-in, spiral-cut hams are selling almost as well as the country hams the family is known for.

City hams can take on water weight from the brine, and some processors inject extra brine or even water into their hams to improve profit margins. It’s important to read labels, because brine (or water) injected into the ham can affect taste and texture.

Top of the line are products simply labeled “ham,” and must be at least 20.5 percent protein by weight. Hams marked “with natural juices” are a good bet, too. That means 7 to 9 percent in additional water has been added. Most supermarket hams are labeled “ham with water added,” which means that the ham has up to 10 percent extra water. Something labeled “ham and water product” can have any amount of water.

Hams with water added can turn spongy, and don’t do well on a spiralizing machine, said R.B. Klinkenberg, chief operating officer of Harrington’s of Vermont.

The company, founded in 1915, bought its first spiralizing machine in the 1980s, after the second patent on Hoenselaar’s original machine expired.

The spiral ham gold rush was on. Harrington’s sent a man with a ham to a spiralizing-machine manufacturer in Detroit to investigate the technology. He came back convinced that the company should buy one. But he also had a piece of advice, Klinkenberg said: If the ham didn’t have a sweet glaze, it wouldn’t be popular.

The company demurred, thinking that a glaze would interfere with its signature flavor, which came from smoking the hams over a blend of chopped corncobs and maple sawdust.

But: “He was right,” Klinkenberg said. “They didn’t sell.”

A method to coat the hams with a maple-sugar glaze was quickly concocted, and the next year they took off.

Hoenselaar, the father of spiral-cut ham, bought the Detroit honey-baked ham store where he once worked from the owner’s widow in 1957. He divided its national territory into four parts and gave each one to a daughter. Decades later, the entire operation landed in the lap of Linda van Rees, a granddaughter, who moved the company headquarters to Alpharetta, Ga., in 2015.

MARCIE COHEN FERRIS, a food scholar and author, was introduced to the cultural significance of the spiral-cut ham after her brother-in-law died and the family gathered at their farm outside Vicksburg, Miss.

“There was a continuous drop-off of spiral hams,” she recalled. “The delivery guy would pull up, hand us a spiral ham, get back in the truck, drive back into town, grab another spiral ham and do the whole thing over again.”

She was in charge of recording the food gifts. “All I did that day was write, ‘Spiral ham from so-and-so.’ ”

Why we glaze

Although the marriage of ham and sugar goes back more than 100 years in the United States, trying to pinpoint the origins of the pairing is a challenge.

Celia Sack, who owns the cookbook store Omnivore Books in San Francisco, found a recipe for ham cured with molasses in the 1879 edition of “Housekeeping in Old Virginia.” Christopher Kimball, founder of food media company Milk Street, found a recipe in the 1890 edition of “The Delmonico Cook Book” that featured a scored ham sprinkled with powdered sugar and baked.

By the 1940s, sugar and ham were so intimately connected that an edition of “The Boston Cooking-School Cook Book” included a recipe for frosted ham in which cold-boiled ham was coated in royal icing.

Pineapple, too, plays a supporting role. The fruit landed on ham as a direct result of marketing efforts by Dole and other companies, which in the early 20th century began urging cooks to use canned pineapple in all sorts of dishes, said Laura Shapiro, a journalist and culinary historian.

In 1931, Irma Rombauer’s first “Joy of Cooking” suggested garnishing ham with pineapple and maraschino cherries.

“Anybody who hadn’t heard of it by that time would have gotten right on board,” Shapiro said. “But even without pineapple, the general rule of making ham as sweet as possible seems to be classically American.”

Some ham makers don’t use a glaze at all, believing that customers want as little added to the meat as possible. Others send along a thick packet of sugar, spices and honey powder with each ham that cooks mix up at home. Companies like Honey Baked Ham hand-glaze every spiral-cut ham with a blowtorch. For most spiral ham fans, the glaze is essential.

“You need that little bit of sweetness with the saltiness,” said Libby Lord, a customer at the Honey Baked Ham store not far from the company’s headquarters in Alpharetta, Ga.