I live in Utah, and your profile says Montana – is that right? So we probably have similar summers, and you probably have colder winters. I get 18 inches of rain a year, most of it in the winter as snow, and I’m in zone 7b.
My summers are very similar to what you described – 90-100 degrees Fahrenheit with almost no rain, except for one week in August (when we get a deluge). No clouds, in soil that is pure sand until you get a foot down, and then it’s pure rocks. No clay at all, nothing to hold soil moisture in. “Full sun” plants tend to do much better in partial shade. I have decided to interpret that as an invitation to plant more fruit trees. 
Common mallow does well in our summers, although it mostly only volunteers in irrigated spaces (like lawns). I can’t remember whether it stays green all winter, or only for most of it – I’ll keep an eye on the one in my orchard and see!
I have found hollyhocks to be even more drought tolerant (they’ll volunteer in completely dry spaces, which common mallow doesn’t), plus they’re huge and therefore produce more food to eat. 
Apparently they’re hardy to zone 3, occasionally as far as zone 2.
For me, hollyhocks sprout in fall and grow actively and lushing all winter, and then flower for most of the summer, and start to die off just as the seeds for next year’s hollyhocks are germinating in preparation for next year’s plants. They’re winter annuals, but you could easily mistake them for evergreen perennials, because they self-sow so easily and grow all year round.
Winter perennials are great for my climate, too. There are lots of bulbs that grow actively through the winter, flower in spring, and go dormant for the summer. Many are just ornamental, but some are edible! For an edible ornamental garden in a climate that’s wet in the winter and dry in the summer, I recommend the drought tolerant mallows (common mallow, hollyhock, okra, rose of sharon, etc.), alliums (garlic, onions, chives, etc.), carrots (some varieties, like Chocolate Dara, were bred to be pretty as well as tasty), tulips (yes, they’re edible! 
), the Calochortus genus (sego lily and mariposa lily), and the Claytonia genus (spring beauty and miner’s lettuce).
Oh, and everlasting pea (Lathyrus latifolius) seems to do ridiculously well here. I used to consider it an obnoxious weed, but then I found out it’s edible, so now I’m happy to have it. 
Apparently it’s hardy to zone 3. The seeds are poisonous raw, but they’re edible if they’re well-cooked – they can cause lathyrism if you eat a very large quantity of them over a long period of time, so don’t do that, but otherwise, they should be safe to eat cooked every so often. The flowers and young leaves are edible raw, and they’re tasty – the leaves taste like peas, and the flowers taste like peas with a flowery aftertaste. I really like them. Keep an eye out for anything in the Lathyrus genus that grows as a weed around you – there are several edible species that are quite tasty and native to our climate, so it’s well-worth watching for them.
You might give fireweed (Chamaenerion angustifolium) a try, too. I just read about it in a foraging book a few days ago, so it’s a new addition to my list of species to try. It looks very promising; it’s a highly drought tolerant zone 2 perennial that apparently has flowers that taste delicious and stems that taste like asparagus.
Speaking of which, if you want ideas of plants you can try that are well-suited to your climate, I strongly recommend you pick up a bunch of books on foraging and look for tasty plants that are native to around where you live. Even if you can’t find wild populations near you, you can go online to buy seeds (or collect seeds from your own wild edibles and initiate swaps with other people around here who have found seeds of wild edibles you’re interested in 
), and they will probably do well.
I swap with other people on here a lot, and I have been thrilled to receive seeds from fellower gardeners who like foraging from particularly delicious loquat trees, particularly excellent nannyberry bushes, etc. As for me, I recently found some thornless hawthorn trees with tasty fruit, and have been saving those seeds to share.
And yes, that is in fact a subtle hint – feel free to hit me up for a trade.
Two foraging books you may want to check out:
This book rocks my socks off. Everything Samuel Thayer writes is great.
This book might be even better for you, because even though it’s less comprehensive, the author lives in Montana. I found it to be a very good foraging book.
And for more ideas of species I’m planning to try next year, I refer you to this post.