There is no good way to make that last.
Flat roof without overhang.
That said overhangs can extend as far as 2 without the need for external supports.
With a flat shed roof the roof simply extends past the wall plate to provide an overhang.
Then the box beams were trimmed out photograph 8 and a double frieze board installed to hide the increase in roof thickness without requiring redoing the gable end siding photograph 9.
Rafter extensions would need to be added onto your existing rafters.
Martin and jon are right that a roof overhang is the best way to protect the siding.
There is also no gutter in the detail so you will be effectively routing rain down your wall.
This is something you can request from your roofing contractor as you plan your roof replacement.
The size of the roof overhang you choose depends largely on the style of your shed s roof.
On buildings where the top of windows are close to the top of the building wall there may be insufficient space to construct an overhanging roof eave without blocking the windows.
This is probably the most costly solution to an un vented no overhang roof design and is practical only in cases where the building is being modified for other reasons.
Most sources i ve read attribute the use of hip roofs with no overhang primarily for withstanding wind especially effective with hip roof usage 100 mph winds etc.
The good news is that a roof overhang can usually be added without having to change the main structure of your roof which is a more expensive and all encompassing job.