Mr. Hamilton, 57, who looks a little like James Taylor, is something of a guru for his wealthy clients, but he has a low-key style. He works barefoot, sometimes in an unbuttoned, well-worn shirt, sometimes with the help of his two sons and stepdaughter. There’s a palpable difference between his bohemian bearing and his bejeweled clients. But he accepts it pragmatically.

“Look, this is the economy out here,” he said. “These projects, these houses, are how most of us make a living.” With the blessing of those who hire him, he delivers surplus produce from their gardens to the East Hampton Senior Center.

Teaching the next generation to appreciate growing one’s own food is important for Ms. Babinski, a professional gardener whose family began operating a farm stand in Water Mill in the early 1970s.

“When a child pulls up a carrot from under the ground for the first time, you can’t beat that smile,” she said.

But Ms. Babinski said she had seen the initial excitement of a vegetable garden fade for some clients.

“They lose interest, though, after they’re planted,” she said. “It’s the same thing with the chickens. They say, ‘I have to have chickens, so I can tell my friends,’ but they end up giving the eggs to the help.”