Edible ground cover for hot dry locations

Has anyone have any experience with edible ground cover for hot dry locations?

Right, not so easy to find!

I have a sprawling rosemary...

And we commonly grow here a plant that covers walls etc, that is the only very green in summer...
Small pink flowers, originaly from south africa... and i can't remember the name nor find any pic in my computer!
And i discovered it is edible... Young leaves are crisp and fresh, for adding in salads. It is more or less crassulae.

Then most of my coverings are in shady or watered places, and I suppose you already have plenty of choice for these places!

Grains generally do well in hot/dry, and are an acceptable ground cover.

Creeping thyme, oregano, marjoram

Anything in the mint family:
basil, mint, rosemary, sage, savory, marjoram, oregano, hyssop, thyme, lavender, perilla, and chia.

I believe some sedums are edible.

Lots of edible cacti, like prickly pear or cholla.