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For early spring, all kinds of leafy greens will do fine in part shade, and it sounds like you get a fair amount of light there. Lettuce, spinach, etc.
Summer is harder. You might try things which like cooler conditions than you normally have in the summer. Otherwise, I'm interested to hear what ideas people have, since I have more shade than anything else!
I can personally vouch for lettuce, romaine, Swiss chard and mustard greens. This year, I've got strawberries growing in both full sun and in partial shade. The partial shade one is a little slower, but otherwise is looking fine and now producing berries -- just a week or so later than the others. On the plus side, the one in the partial shade may last longer into the hotter season.