Are we looking at the bottom of this big pulley?
Turn a bush to nominal size, (OD a bit larger than what you will need to bore out of your pulley to get rid of the damage). Bore the bush and cut a keyway, then I would look at turning a press fit collar that will go over the exposed end of the protruding part, this to provide some support for when you machine the old keyway out. (This will depend on how deep the keyed section is, If there is plenty of material up in the pulleys' then the collar may not be neccessary but if the keyed section is relatively short then you might need to consider adding some "meat" Bore the pulley to accept your new keyed bush. Press it in. Depending on access you may be able to drill cross wise (or close to it) to secure the new keyed bush to the pulley, or use a "dutchman". Or weld.