Lettuce, herbs, onions and other alliums. I'm sure there are more and that other gardeners will tell us.

Carol

If you search 'shade gardening' here you'll find several discussions if interested as that is basically what you would be doing - shade gardening. Lots of info on Goggle too using that search term.

But they usually boil down to the same things - those that Carol listed above. I just add all kinds of leafy greens - kale, cabbage, chard, spinach, bok choy, etc.

Dave

Sounds like you know what loves the heat & it's basically everything else that grows in part sun/shade. If your 3 hours are mid-day you'll have no problem growing vegs. Slower to warm in spring, but slower to heat up in summer, so still good for growing some veggies.

Dappled high shade is different than dark shade from a building.

In partial shade harvests are slower coming & smaller, so plan on planting more; however, there are some advantages because you can grow lettuce all summer with great taste, less need to water, less sprouting of weeds, vegs wait a bit longer before harvest is needed (less bolting), and more comfortable to work in the garden. Often less bees, too, which is more for the squashes anyway.

These grow really well for us to use in salads & stir fries: swiss chard, spinach, chives, allium, pansies, pot marigold (Calendula), Red Russian kale, lettuces, zucchini, & parsley.

Last year some zucchini were crowded under part of the pear tree & though slower to produce those 2 plants produced longer in the season, so shade can be an advantage.

Moderate results with broccoli, kohlrabi, pak choi, & red cabbages as they take nearly a month longer to harvest. Broccoli keeps producing side shoots all summer in part shade without bolting.

There are good things from shady places, too.