“It was this ginormous green spectacle that came on a tray, at least 12 inches tall, and it was very intense,” Ms. Chung recalled. “I was shocked how it kept its shape despite having all this syrup.”

She compared the texture of perfect kakigori to flower petals — not quite powder and not quite grain — making it distinct from other kinds of shave ice. “It’s a simple thing that’s really hard to execute,” Ms. Chung said.

Stonemill serves a traditional kakigori, ujikintoki, doused with matcha syrup and finished with a touch of sweet red bean paste. Every day, the restaurant’s pastry chef, Mikiko Yui, makes coffee jelly and soft mochi to garnish it. The cafe will keep the dessert on the menu through early October.

Cha-an Teahouse has been serving ujikintoki and other kinds of kakigori in New York for more than a decade. Ms. Uematsu drew from her own experience with the sweet as well as her training as a chef to develop the white peach kakigori made from poached fruit and decorated with chewy, housemade peach gummies, cut into the shapes of stars and hearts.

As he prepared to open the David Chang restaurant Majordomo in Los Angeles in January, the chef de cuisine, Marc Johnson, learned about shave-ice culture through local Korean and Taiwanese shops (cultures which also have rich histories of shave ice) as well as a popular Instagram account run by Margaret Lam.

“She’d go to these kakigori competitions and jams where people would just get together and show off their craft,” said Mr. Johnson, who does not employ a pastry chef and was eager to figure out the technique.

He found that the more delicate the shavings, the faster they melted. Kakigori makers often press the ice very gently with their hands, giving it a distinct rounded shape; but if packed too firmly, those soft, feathery crystals can freeze together as hard, wet clumps.