VIDALIA, Ga.—On a recent visit to a Thriftway supermarket near this onion-growing center, Aiden Harvill spotted a jolly green giant at a bin stuffed with Vidalia onions. "Mama, there's Shrek," the three-year-old shouted. He then threw a tantrum until his mother plopped a bag with Shrek's image into her shopping cart.

"He never, ever eats vegetables, but when we got home, he wanted me to cook them," Elizabeth Harvill says. She diced the onions into a casserole, which Aiden gulped down. "I was astonished," Mrs. Harvill says....