Ticks all the boxes for me.
Letting them to go cold actually means the excess water has been allowed to steam off.
But I don't bother peeling before boiling. It's so much easier after boiling.
Also since a lot of flavour is in the skin, although you remove it - it adds to the flavour to the...
Par boil with skins on THEN peel.
They are easier to peel when cooked. It comes off with a blunt knife (*)
Allow to completely cool in sieve / colander.
Shake about a bit in pan to rough up edges.
Cook in whatever fat you like, but tray with fat fat must be heated in oven beforehand.
(*)...