I have a shaded area too. It gets tricky because powdery mildew loves the shade. You live in a much hotter place than I do, but the shade living things I've found are peas, cucumbers, chard, spinach, radishes, and my carrots did well. Most of those would probably be winter crops for you. The beans did well in the shade, though they'd have liked the sun more. I also had arugula there, which did ok. Rhubarb does ok with shade, but it needs a lot of room. I'm also growing gooseberries and raspberries in partial shade. I've heard bok choy does excellent in the shade, though I haven't tried it.
