How to model rounded extrusions I am trying to create sci-fi doors similar to those that Dan Brown creates below:



I have tried a few methods, the closest I can get to the image is using a solidify modifier and then making edge loops and cutting away faces.

This method only gives me curves on the outer edges, I would like to have the inner corners curved also, cannot seem to find a way to do this.



Can anyone think of any ideas to try?
Well thanks to brasshat answer, I played around a bit and found one way to achieve this, there may be a better way but this certainly gives decent results. 

I used the bridge edge loops tool.