"I'M A CAPITALIST, I'm a CEO, I run a big business, I'm an employer," says Sophia Amoruso, the 29-year-old head of Nasty Gal, the online fashion retail empire that she transformed from an eBay vintage store into a $240 million company in just seven years. "But it's all secondary to the way it happened, because I could be anything."

Sitting in the back garden of New York's Crosby Street Hotel dressed in a crocheted lace dress and a trench draped over her shoulders, Amoruso is reflecting on the period of...