Customers at Tenuta Vannulo, in southern Italy, know they better come early to snag a number before the cheesemaker's specialty sells out. After all, this is fresh buffalo mozzarella.

Mario Spatuzzi came all the way from Milan, seven hours away via train.

"You can buy this in the grocery store – why come here?" asked correspondent Seth Diane.

Mozzarella to die for. CBS News

"Because the taste of this one is simply amazing," Spatuzzi replied. "This is made of the buffalos that you see over there, just behind this shop."

Customer Josh Miller has his priorities when it comes to the cheesemaker, which is not far from the ancient ruins of Paestum. "Maybe we'll get to Paestum, which is the temple, but this is the first stop!"

The crowds turn out for the fresh mozzarella at Tenuta Vannulo. CBS News

Staff pack the fresh buffalo mozzarella in Styrofoam boxes. Emotions, however, are not so contained, as some women began fighting over their turn in line.

Nicola Palmieri runs his family farm, where the buffaloes are pampered. "If we can give them the possibility to live in the best way, we must," he said. "And the technology gives us this opportunity."

Soothing music is piped into the pens, and when the buffaloes feel they are ready, they line up on their own to be milked by machines. They can also take a shower, or get a massage.

Pampered buffalo, the source of buffalo milk for Tenuta Vannulo's cheeses. CBS News

"They have to be relaxed," said Palmieri. "This is one of the secrets that we use to make a good mozzarella."

At the caseificio (or cheesemakers), the milk is collected, a curd is produced, and in just about five hours it is formed into balls, with the special technique that gave mozzarella its name. (Mozza means to cut.)

Cheesemakers at Tenuta Vannulo. CBS News

The chance to see the process draws locals and tourists alike, including Patricia Oakes from Louisiana.

Doane asked her, "How different is the mozzarella you've tried here in Southern Italy from what you've had in the U.S.?"

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"Oh my gosh! It, like, melts in your mouth!" she exclaimed.

Buffalo milk has a higher percentage of fat than milk from cows, so it's richer and sweeter.

Domenico Caldarone came from Bolivia to learn this rather involved art, at the Consortium for the Protection of Buffalo Mozzarella in Campania.

Doane asked, "Did you realize how difficult it was going to be to make mozzarella?"

"No! No, I was thinking this would've been more like a one-month process," he replied.

But it's been six months and counting.

Domenico Caldarone learns art of cheesemaking at Consortium for the Protection of Buffalo Mozzarella. CBS News

Doane said, "It looks easy!"

"Trust me, it's not," said Caldarone.

Complicated to master, but whether featured on a pizza or eaten plain, it's simply delicious.

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Story produced by Mikaela Bufano.