Not quite the same but I make salted duck eggs which are lovely (I think). I used to sell a lot of my eggs to a Phillipino woman I worked with as they are a bit of a delicacy and apparently just not the same with hen eggs.
Make a supersaturated salt solution (deep adding more salt until no more will dissolve and there are undissolved crystals at the bottom.
Place UNCOOKED eggs in a jar and cover with the brine and then leave.
When ready to use, take them out and boil them as you would normally for a hard boiled egg and eat as desired!
Ater they have been in the brine for about a week then have a pleasant saltiness and are usually chopped into salads etc. If you leave them for longer (up to a month or more) the yolk starts to change texture and become waxy. The white becomes unpleasantly salty and is usually thrown away and the yolk which really don't taste that salty are eaten or used in something called Mooncakes (which I have never done so don't know anything about).
I like them much more than pickled eggs but maybe an acquired taste.