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Hello @ELI5
Thanks for sharing your question about your fascia. In this particular instance, I suggest engaging the services of a tradesperson or builder. They will do an Indepth investigation on how far the rot has travelled into the fascia. If it has affected the entire piece or more than 3/4 of its surface, it would be better to replace it than trying to repair it.
In regards to covering it, Colorbond is also a good option. If the Colorbond fascia is properly mounted and does not leak or bridge water over to the other timber surfaces, it should provide a long service life. Depending on your budget, I propose getting a quote from your builder on how much it will cost to wrap the fascia in Colorbond.
Let me call on our experienced members @Dave-1 and @Nailbag for their recommendations.
If you have any other questions we can help with, please let us know.
Eric
Morning @ELI5
Whoops lost the post lol When I went to check your pics I closed the tab... Shaking my head 
The steps @EricL has suggested are the ones I would be following, finding out how far the rot may have travelled is a good place to make a decision.
My mums eaves (looks very much like yours) had rot at the same point, It was onlly bottom 500mm that was rotted. The builder chopped it off square and replaced it. You can see a slight difference in sizing but she is happy with it.
I would rip a larger width piece down to match exactly the bit you cut out. You may need to go up the eave to make sure you have enough attachment points to secure the new section.
Dave
Hi @ELI5
Rotting Oregon facias/eve boards is common and one I have to deal with on a regular basis. Before and after photos attached below.
You have two options:
1. Short term (selling in the next couple of years). Cut the eve board back past the rot, apply Earl's wood hardener to the end of the kept section and add a new section. Though challenging for the less experience, a doable DIY project
2. Long Term. Replace the entire eve board with new in either H3 treated pine or colourbond. Colourbond only if you're going to replace both sides so it matches. And to be clear, the colourbond option is a replacement not a wrap. That doesn't fix the issues, just hides it. Its also a more difficult project and one I would recommend getting carpenter to tackle. The roof flashing will also need to be removed and replaced.
Nailbag
