Planning cob building for later addition

Now I understand the issue.

if the lime plaster keeps the inside of the wall from getting wet, why are overhangs so encouraged?

Wetness and moisture are two different things
Simply put, water has a few forms;
- wetness may flow out of a pipe
- moisture may be floating in the atmosphere.
- you can feel and see wetness as a liquid
- moisture is in the form of a

All liquids are fluids, but not all fluids are liquid

Lime plaster is protective, but if a large amount of water gets on the wall, it may penetrate the plaster layer and get to the wall material and weaken the wall/plaster interface and get to clay based material, so it's wise to protect such a wall with overhangs.
Have you thought about a roof window with an interior shutter? You could keep protective overhangs (if unstablizied wall) and have direct sun heating option, easily controlled by the shutter?

John, are you saying that the lime plaster is meant to protect only against humidity and not rain?

Cristobal, I've seen that some adobe houses have a cement plaster on the lowest portion of the wall (about a meter), and a natural plaster above that. The window is an interesting idea. You're saying that the sun would cross the window, and heat the norther wall? I've thought about a skylight (I don't know if these are the same as roof windows) with an interior wooden door/shutter that can be closed in the hottest months.

Your idea made me think of a removable or retractable awning. In the months here when the sun is low enough in the sky to warm the walls, it generally doesn't rain. The awning could be extended or installed before the rainy season.

I meant skylight, but did not want to call it this way, because I associate them with something without interior shutter and even not openable.
Awning can be easy torn by winds, and in my opinion would be short lived.