This is how it began, the career of one of the most versatile, ingenious and adventurous chefs in the history of American cuisine. Jean-Georges Vongerichten can pinpoint the day, the place, the words. "My father liked to talk," Mr. Vongerichten recalled. "He already had three glasses of wine, and he said to the chef: 'My son is no good. Do you need somebody to wash dishes? He will do it.'"