Anything which you primarily eat the leaves or
roots of, instead of the fruit. Fruit-producing is what usually needs the most sun.
So:
Salad greens: Arugula, lettuce, sorrel, endive, spinach, collards, kale, mustard greens swiss chard... any of those 'mixed greens spring mix' seed packets.
Roots/Stem Base: Beets, Carrots, Potatoes, Radishes, Rutabaga, Turnips, radicchio, Kohlrabi
Flowers: Broccoli, Cauliflower, brussel sprouts, cabbage
Herbs: Mint, chervil, chives, coriander/cilantro, oregano, parsley, thyme, oregano
Rhubarb and Asparagus also seems to tolerate partial shade/dappled shade, but they will be slow to mature and so you may not be able to harvest from them for a few years, until they get well-established.
While none of them like DEEP SHADE, I've had decent luck with most of these growing under the edge of a tree
canopy.