I've put a few Miners Lettuce (Claytonia perfoliata) plants in my AP system and they seem to be really happy so far. I'm pretty sure it's classified as a perennial, although I don't think it grows for as long as some other perennial greens. You can use it as a salad green or cook it like you do spinach or silverbeet. It's quite high in vitamins and minerals too (it was used by miners in the gold rush in the US to ward off scurvy and brought to Australia where it's naturalised in a lot of old gold rush towns).
You can get seeds from quite a few online stores if you are interested.
