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.
some ideas...
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