Maybe there’s an easy solution without addons, but it shows there’s a lack of fillet function in Blender, something i hope the devs will include one day (or at least as a setting of the vertice bevel function).
But you can try this, assuming you’re using a buildbot or 2.72 RC as the required addon is only in contrib addon that do not come with so called “stable” releases (if not you can download a buildbot version here or 2.72rc here ) , go to file -> user prefs -> addons and in the “Testing” category, enable Mesh : Extra Tools.
Now back in Edit Mode you have your mesh setup like that without inset :
In the toolshelf, click on the Mesh Extra tools “Face Inset Fillet”
Press F6 (or look in the operator panel, bottom of toolshelf) and tweak the settings until you’re satisfied
Thanks for the great answer Sanctuary!
i was using v2.71 but upgrade to the RC 2.7.2 to try out this addon and it is a great help. Exactly what i was looking for, i can see this begin a very useful tool!