“It is doable, but it is not easy,” said Alberto Gonzalez, an owner of one of New York City’s first certified organic restaurants, Gustorganics, which operated from 2008 to 2015. Each dish, for example, involved as many as 25 ingredients, and all of them had to be organic; but some ingredients had only one source — a farm or producer — that could supply an organic version.

“If there was a shortage, we were struggling,” he said. “You have nowhere to go.”

Ashleigh Knecht, a certification coordinator for the Northeast Organic Farming Association of New York, said the regulations seem tailored more for farms than for restaurants, so it could be difficult to figure out how to apply them to the restaurant setting.

For many diners, organic certification of restaurants doesn’t seem to matter much. Some even distrust the designation.

“What’s more important to me is the restaurant’s mind-set and attitude toward the food chain,” said Noah Youngs, who was having lunch recently at a Bareburger on the Lower East Side. “People earn the label ‘organic’ all the time and still have terrible practices.”

Timsie Malaney, a cardiologist at another table, said she preferred that restaurants list their meat and produce suppliers — as they do on the Bareburger menu — rather than point to their organic certification . “It’s just a label,” she said. “They are not telling you where the product is coming from.”

The Department of Agriculture doesn’t plan to change its rules to require restaurants to seek organic certification, an agency spokeswoman said . If customers are skeptical of a restaurant’s claim to be organic, they should submit a complaint through the department’s website, she said.

Mr. Rosenberg filed one last November about Bareburger, and didn’t get a response until May, simply confirming receipt of the complaint. He said he hasn’t heard anything further.