The cow shed with an 8-foot span is intentionally left unplastered, because visitors were convinced that there was some structural secret other than earth in the roof of the battery house.
We intended to remove the wood planks, but it doesn't seem that will possible. The low arch seems to exert too much outward pressure on the walls below it, and they seem to be leaning away.
I'm dubious about combining a living roof with an earthen roof. The reason our cob roofs survive is because our climate is so, soooo, very dry. Even though a living roof would have a waterproof membrane under the soil, you have to expect that sometime in the coming decades it will spring a leak.
Again, the thermal comfort is wonderful, and we attach a greenhouse on the south side in winter, and keep a small vent hole open at the top, and still two cows keep their own shed at a minimum of +16C (+60F) when winter nights go down to -23C (-10F).