Shaved ice must be an ancestor of
sherbet, now promoted by its more expensive name
sorbet. It is simpler than sherbet, however; it is basically a snow-like mass of finely ground or
planed ice with some flavoring poured over it.
Growing up in New York you could often get Italian ices in little pizza places, where plain shaved ice could be flavored with a small choice of colorful fruit concentrates. (Anark has described the same sort of thing as a "snowball" in Baltimore.) I remember that my mother thought it was a fine substitute for ice cream, and so naturally I disdained it. In Caribbean neighborhoods, when I got old enough to wander there by myself, there were pushcarts on streetcorners offering a more exotic menu: ices flavored with sodas, tropical fruit joices, or even alcohol could be bought if you knew where to go. As with the Italian form, you had to be careful not to suck all the flavoring out too soon, otherwise you'd be left with boring ice shavings to finish. But with all this in my background I was not prepared for the experience of shaved ice that confronted me in Taiwan when I first went there in 1984.
Even in a big city like Taipei, bau1-bing1 or "planed ice" was a mainstay of the Taiwanese sweet tooth in the days before Western style desserts invaded the island. There were all sorts of establishments selling it, but I lived near a small one and got to know how they did things. A big block of ice would be delivered to the floor, and the young men would set to work on it with planes, shaving it down into masses of white snow, over which a great range of toppings could be poured. Foremost were the sweet cooked red beans that I've described at Chinese concept of sweet vs. salty, but there were various other starchy or fruit-based toppings, including preserved guava, mango pulp, pineapple, sweet lotus seed, and so on and so forth. In the ghastly hot summer, a food like this did you a lot more good than cheesecake possibly could. I suppose the people in Sicily and the Caribbean feel much the same way.
In my younger days in Taiwan, a lot of foreigners didn't like ices. You thought about the cleanliness of the floor, and the hands of the young men, and the fact that no one in Taiwan ever drank water unboiled, and then you usually cast your health aside and ordered an ice. But you were sometimes served it even in fancy restaurants - the "seafood king" Hai3-ba4-wang2 used to bring you a brilliant green salty-sweet preserved mango ice with your check, and I never saw anyone turn it down.
When I got to know some people in Ilan, a rather independent-minded little town on the long-isolated north-east coast, I was introduced to a storefront with no sign, called by everyone Oo1-tiam3, "black store". The store sells a kind of dense snow, produced in just a few traditional flavors - the bestsellers seemed to be peanut and taro, mildly sweet but intense. The peanut version is the single food I most miss from Taiwan. I do not know how they make it, but it seems the flavoring substance is actually frozen into the ice before it is snowed, with the result that you are never left with boring ice after all the flavoring is gone. The Taiwanese name for this form of shaved ice is sng1-a2, the diminutive of "frost". Sng1-a2 was even sold in the countryside when I first got there, by people who dispensed it under umbrellas from old-fashioned tubs insulated with straw.
These "frosts" are actually more than shaved ice - they are no less than a form of sherbet (oh, call it sorbet if you must), and are apparently representatives of a type known in rural Taiwan for at least two or three generations and perhaps many more. They are immensely popular in Ilan, although in spite of Oo1-tiam3's financial success the owners seem not to care about putting up a sign. There is an ancient business license posted on one grimy wall, so I guess the place is legal. Either that or the police know better than to mess with them. Taiwan police are nothing if not practical.