Cob building
...Some people have called it monolithic masonry. Unburned clay masonry is another name for it used in the uniform code book. I was referred to Volume 3-357 for cob wall standards and 21-9. Thermal mass rather than insulation is the key as with adobe but cob is thicker. Still, in extreme heat and sun, it may be too warm by afternoon.You could shade it or do infill with strawbale for more insulation. Working with the mud and straw of cob is therapeutic compared to more technical building like strawbale. A freeform cob sculptured house with many tiny windows is charming

Underground storage ...Another dream of mine because the sun and heat damage more stuff in the Southwest than other kinds of weathering. Shade and cool storage for gardening materials would be great in an underground structure.
...If we insulate the deck roof and put a simple carport roof over it as a work area, the deck and the underground area would be protected from the monsoons and the summer sun. And dirt from the hole could be used to build up berms (thick low banks) to control/ collect rainwater.

Straw Bale Foundations in Pima County, Arizona require a large amount of concrete, especially in A01 where buildings must be 24" above grade.

...An owner-builder in Pima County said he scrapped his straw bale plans because Pima County requires a concrete footing below the bales the width of the bale down to one foot below ground level raising the cost of the foundation from one to $4000. I would rather build a free-form cob house with straw bale as the back wall on the shady north side and maybe the sun side too.
...I understand now why people plunk down mobile homes on their ranchettes, especially those on the flood plain. Everything from the permits to the site built house itself is involved and expensive, especially once you get away from "stick" houses. I cringe when I see the amount of wood and toxic materials used to build a conventional house.
...Still, though it would take longer and cost more, lower energy costs for a straw bale or cob house would make up for it in a few years. And the strawbale shell would provide instant insulation as a work area from cold and heat before the expense of the roof..