Common Nature

i don't have much personal experience with that much shade, but remembered reading about this collection:

Shady Garden Collection
Most vegetable crops like sunshine, but we don’t all have perfect conditions to work with. We’ve gathered a selection of vegetables, plus one herb, one edible flower, and one berry, that will survive some shade and still give a worthwhile result. Also useful for coastal and cool-climate gardeners. Info sheet included. Contains one packet each Asian greens, chard, runner beans, kale, spinach, lettuce, chives, radish, sorrel, peas, nasturtiums, chervil and currant. 13 pkts.

from http://www.bountifulgardens.org/prodinfo.asp?number=LSH-6755