It was Friday, Feb. 2, 1962, and President John F. Kennedy summoned his press secretary Pierre Salinger into his office for an urgent meeting.

"I really need some help," said Kennedy.

"What do you want, Mr. President?" Salinger replied.

"I need some cigars," JFK replied.

"Fine," Salinger answered. "How many do you need?"

"A thousand," said the president.

Kennedy didn't need a thousand of any old cigar; he wanted H. Upmann Petits, his favorite. He also wanted them before the following morning. In Kennedy's desk drawer was Proclamation 3447, which would slap an embargo on all U.S. trade with Cuba. By 8 a.m. Saturday, Salinger came through with a shipment of 1,200 Petits, and the president signed the embargo into law.

Even if you're not one of the estimated 12.6 million Americans who smoke cigars, there's a good chance you've heard of H. Upmann, which has come to embody all of the privilege and decadence of its category. Winston Churchill was known to include H. Upmanns in the 10 cigars he smoked daily. Milton Berle tried to get 500 of them into Paris on his honeymoon. Upmanns are, said one reviewer, "as famous a brand as there is."

"In addition to being a great name, it's a quality product," added Janelle Rosenfeld, marketing vp for Altadis USA, H. Upmann's American distributor. "Three hundred pairs of hands are involved in the making of each cigar. We were the original artisanal product."

In 1844, German banker Herman Upmann took a trip to Cuba, fell in love with the local cigars and started a proprietary brand he gave away to his investors. Upmann's cigars were so popular that they outlasted his bank.

But thanks to JFK's trade embargo, there are actually two H. Upmann brands these days: the ones made in the Dominican Republic that Americans can buy and the ones made in Havana that they can't. The fact hasn't diminished U.S. demand for the brand, nor hurt its mystique—in part because the leaf blends for varieties like The Banker are painstaking matches of the original, and easily command $125 a box.

Still, purists believe Cuban cigars should come from Cuba. With President Obama's relaxing of the trade embargo in December, puffers are hopeful that they'll soon be able to light up a true Habana. (For now, visitors to Cuba can take home $100 worth of cigars—a fistful at most.) "How it will all unfold, nobody knows," Rosenfeld said. "But it raises awareness, and that's exciting."