Great list here. http://backyardlarder.co.uk/plants/perennial-vegetables/
I would add 4 - they are all roots so they are only perennial by replanting a tithe :
Yacon & Oca - pretty much flavour of the month - look them up. Good yield.
Rampion - beautiful lilac/pink bell-flowers and small, smooth, white tubers but delicious, sweet and crispy for salads. Plants are small (two years were as long as I could keep my hands off them) so you need to grow a lot - expect a quarter the yield you'd get from the area. I'd be interested to hear from anyone doing better.
I don't know if they grow from tubers - they are too delicious.
Lathyrus tuberosus - tubers taste like sweet chestnuts - the only 'sub' vegetable that is anything like the real thing (all the asparagus subs are a bad joke*). Unfortunately it rambles - too weak to be a real weed but best grown in a trench lined with plastic (pierce the middle of the bottom only) - because otherwise you won't find the damned dark thumb-sized tubers against the dark soil. They grow even better (to medium yield) in rotted woodchip (lined trench or builders bag) - and then they are a lot easier to find. They will grow from tubers or any even slightly lumpy root strings you can't eat.
NB. the lined trench is the only sensible way to grow chinese artichokes - delicious but a real weed if they escape.
Cheers.
PS* Also
Hop shoots are delicious
treated as asparagus, and well worth collecting - they just don't
taste anything like it - all the other 'subs' are tasteless (or just plain horrible).