The last two food banks I have volunteered for have been very active in growing fresh food. The current one has about 2 acres of ground that they are farming. Plenty of our volunteer workers are also our clients.
The previous one had a relationship with the local Master Gardeners who managed the local community garden plots. As well as "leasing" out plots (IIRC, the charge was $10 annually for a plot), the Master Gardeners reserved three plots for growing for the food bank, and usually took over 2-3 leased plots where the gardeners, for one reason or another, were unable to take care of their plots.
Then there's the grandaddy - Will Allen
Growing Power | Together We Are Growing Power
And cities are getting involved too -
P-Patch Community Gardening - Neighborhoods | seattle.gov
Lots of different ways to go at this. These efforts just need a spark plug...