You can only eat so much Swiss chard, so I don't know how much you'd want to plant, but mine is growing happily in a fairly heavily shaded spot in the garden. It doesn't grow as fast as in the direct sun, but it also doesn't suffer that horrible mid-day wilt, either. A friend of mine told me of chard being used as an edge plant around gardens at the Dallas Arboretum - that sounds beautiful - but it is also quite delicious.
Peppers also grow a little slower, but they do grow. My best plants don't get sun after 3pm, and my so-so plants in the front in more shade produce nice fruit but at a slower rate. If I paid more attention they might do better, but the point is, they do grow. And there are lots of herbs that will grow in a few hours a day direct sun. The lemon balm in my back yard only gets afternoon sun and grows like crazy (it escaped from a pot and has been prolific back there ever since.)
You can grow garlic, though you won't get very large cloves, and you can grow onions. Just don't try for the plants that have their highest production in the high heat and bright sun of summer (okra, eggplant, etc.)