East Village entrepreneur Bon Yagi might not have introduced okonomiyaki to New York when he started serving the savory Japanese cabbage pancake at his street-food shack, Otafuku, in 2000, but he certainly popularized it. (Earlier sightings do exist: In a 1988 review of Oyshe on the Upper West Side, former New York Times critic Bryan Miller referred to the “light and healthful style of cooking called okonomiyaki, which the restaurant bills as health food for the samurai warrior,” and described the version he sampled as “intriguing for the texture but, on the whole, bland. A good dose of salt and pepper or fresh herbs would make all the difference.”) Miller and even Yagi, who relocated and expanded his shop (now Otafuku x Medetai, 220 E. 9th St., nr. Second Ave.; 646-998-3438) earlier this year, probably wouldn’t recognize today’s riffs on the actually not so healthy dish whose very name invites tinkering. Okonomiyaki, which has been compared to pizza, latkes, and omelettes, translates to “as you like it, grilled,” and in Japan, diners choose what meat or seafood they want incorporated into the flour-and-egg batter. Its defining characteristics include its texture (crisp outside, gooey within), its agreeable greasiness, and its distinctive garnish: squiggles of Kewpie mayo and a sweet ketchup-soy-Worcestershire-type sauce, a sprinkle of nori powder, and a blanket of shaved bonito flakes that flutter from the heat.