As a master gardener, Gary Oppenheimer knows how to grow a bumper crop of cucumbers. Problem was, his wife was so tired of eating cucumbers, she told him not to bring anymore into the house.

So Oppenheimer, a New York resident, donated his extra gard­­en produce to a local women’s shelter. Folks at the shelter kept thanking him for the fresh produce, a rare treat when most food donations are canned fruits and vegetables.

From this exchange, Oppen­heimer came up with the idea to start a website to connect gardeners and farmers with extra produce to local pantries that provide food to families in need.

The website, AmpleHarvest.org, has since become a nationwide food-relief network that’s been recognized by...