Not enough timber on my land to try that yet. I have a plan that I think will work, I just need to run it by the Building Inspector first.
I can get the frame for a metal carport fairly cheap. My plan is to start with that, wrap the outside in wire mesh, then cover the mesh with fabric that’s been soaked in concrete. A second layer of wire mesh/fabric/concrete on the inside of the frame, with a gap between the two layers of about 6 inches. Fill that gap with concrete that has insulative materials mixed in, and the result should be pretty solid.
I have different recipes for the concrete used in each layer, so the outer one would be waterproof and the inner one would be mold-retardant.
If things get bad before I get it finished, I know how to make concrete from natural materials. It’s a lot more work than just buying it in a bag, but it can be done.
If you do not already have it there is a good book, "The Owner Built Home" by Ken Kern. (A picture of it on page 242.)
He discusses concrete with cob materials or rice hulls.
You could also use styrofoam beads. Or something like:
https://www.youtube.com/watch?v=2OUgqlzDIrw Foam concete.
There are also log cabin kits, but they are not light.
Whatever you decide I hope it goes well!