In response to the original question: What can I grow without irrigation?
In my area, we get about 25" of rain per year, Oct-April. The summers are not very hot and nights are cool. Swiss chard, tree collards, blackberries, artichokes, fennel, and feral brassica mixes all grow wild in the uncultivated areas of my garden, and they make it through the summer. The mulch layer is fairly thick, but other than that they receive no care. They seem to do best surrounded by a living ground cover.
Some work well if they are planted during the rainy season and then finish maturing in the early summer without irrigation: potatoes, quinoa, garlic, peas, onions. (Also with a thick layer of mulch.)
I have had tomatoes thrive without water if they are right next to a compost heap, which is kind of similar to the principals behind hugelkultur.
This is an area with only a few light frosts in December, so we can grow cool-season crops during the rainy season without irrigation.