Why is my cottage wall bulging outwards?
Disclaimer: Consulting with an engineer is highly advisable.
The roof is slowly pushing the wall outwards. If you have not purchased this cottage yet then either walk away or low-ball them. I foresee that subcontracting a proper fix easily reaching $10k.
You need to do two things:

Straighten the wall out
Prevent the wall from bowing out in the future

To straighten the wall out I imagine you would need to attach a bunch of steel cables on the inside of the cottage and tension them enough to pull the walls inward.
For preventing future bowing you have two options really:

Brace the roof from the outside
Tie the roof together from the inside

Whether or not this is a project you can take on is up to you.

Option 1:
The red lines are extensions of the roof line; you can use pressure treated wood or preferably steel beams. The white circles are concrete footers.


Option 2:
The red line is a bracing inside the house which should prevent further separation and bulging. There should be several of these running throughout the house.


I'm not sure why the inspector suggested a concrete pilaster since your foundation does not need bracing but rather the exterior wall but then again I'm not an expert.
Good luck to you!