Rot in Summer house overhang

[prologica]

HI all,
I’ve got a 4m x 4m summerhouse with felt shingles over a softwood (pine I think) plank roof around 28mm thick. The roof overhangs the walls in a Swiss chalet style.
I’ve found significant undetected rot in the planks where they overhang. Otherwise they seem to be in good condition. Is there some way I could remove the rotten areas and ‘patch in’ some new timber? The issue I see is that being an overhang there is nothing to support the new timbers.
Any bright ideas?
Thank and have a great Christmas!
David

 

[big-all]

is the rot on top or underneath??
if its underneath you need to stop the source off damp/wet first