Fava beans and Barley are hardy in zones 7-10. Wheat is hardy down to zone 5.
The gluten-free grains (sorghum and teff) are summer cover crops.

Cover Crops that are Food Crops

Fava Beans (Broad Beans)
$2.95
$2.95
Hard Red Winter Wheat
$2.95 - $7.95
$2.95 - $7.95
Agricultural Mustard
$2.95
$2.95
Dale Sorghum
$2.95 - $19.95
$2.95 - $19.95
Brown Teff
$2.95
$2.95
Ivory Teff
$2.95
$2.95