Remember when the word mozzarella evoked shreds of dry string cheese? When "fresh" mozzarella in cloudy water finally usurped Polly-O? And then, not too long after, someone served you even milkier, pricier stuff called buffala? Well, Italian cheese antes have risen. Today, the ultimate mozzarella has more flavor and textural complexity than anything on a pizza. Call it "burrata." Then find a restaurant sourcing it from Puglia or Basilicata, the Italian regions that make it best, and eat it, at least initially, adorned with nothing but olive oil, seasoning, and maybe some grilled ciabatta.

First made from buffalo's milk, and now also the product of cows, with a refrigerated shelf life of only a few days, burrata is to mozzarella as Parma prosciutto is to ham, and it's currently flooding better menus. To make burrata, an artisan forms fresh mozzarella, but the center, or burro ("butter," in English), receives a filling of the cheese curd strands (called stracciatella), which are left to absorb the whey's fresh cream – a classic Italian method of spinning waste into gold. The result: a pillowy ball of white goodness tied with a knot and filled with a velvety core that oozes when cut.

Burrata is so popular now that a Pugliese-born cheesemaker – Vito Girardi's Gioia Cheese Co. in El Monte, California – makes and ships it domestically, along with Dallas's Mozzarella Company, Vermont's Maplebrook, and a few others. At the same time, top Italian restaurants like Nancy Silverton and Mario Batali's Osteria Mozza in Los Angeles consider burrata the centerpiece of their mozzarella bar, offering the California product as well as an imported burrata from Basilicata, Italy.

"The texture is so luscious and sexy, but it's very milky, and the flavor is still relatively mild, so it's delicious alone but also pairs with many flavor profiles," says Silverton, who marries her buttery Italian import with nothing more than stewed leeks, extra virgin olive oil and ciabatta, but offers the milder domestic Gioia with speck, English peas, and mint; or marinated escarole, applewood-smoked bacon, and caramelized shallots. "There's a definite increased awareness in burrata throughout the country," she adds.

The fresher the burrata, the better, say chefs, even if they still believe in the ultimate superiority of the Italian product. "We did it from the start from Puglia, and we're able to get a shipment sometimes twice-weekly," says Chicago burrata expert Tony Mantuano of Spiaggia, who calls it a great caviar base. "It's an opportunity to provide something elegant and authentic, recognized by the Italian government, that a lot of well-traveled, four-star restaurant-goers have eaten."

At The Ritz-Carlton, Key Biscayne's Cioppino restaurant, burrata proponent and chef Ramon Guerrero prefers his cheese with crispy haricot verts and good Tuscan olive oil. But Guerrero's quick to point out a foodie's passionate exaggeration. "I wouldn't necessarily call burrata a trend, as I think it's here to stay," he says before offering caution upon hearing an anecdote about a rogue Whole Foods workers who called burrata "just mozzarella filled with marscarpone." He adds: "Be very aware of imitations, as stores in the U.S. are still pretty unfamiliar with the true thing."