So I have a box that gets about 3.5-5 hours of light max depending on season. I have found that with Broccoli, the plant gets big, but the heads take longer to show up and are about half the size of a full sun plant. Bush Beans produced good with a marginal decrease in production, and I actually had some of my biggest carrots out of that box. I just had to leave them in a bit longer. So I guess in my opinion Carrots are the best, then bush beans, then broccoli. I have no opinion on Potatoes yet.

In order of best IME - beans, carrots, potatoes, broccoli. Agree with what jeff said about the carrots need to be left longer, the broccoli heads will be smaller (1/2 size) the potatoes will be less and smaller. What does better than any of them in shaded areas is leafy greens - lettuces, spinach, chard, kale. even some cabbage.

Dave

Certainly
worth experimenting to find out what the partial shade area will do. I have a strip along the west side of the
house that gets an absolute maximum of four hours of sun per day (approx.
Noon-4pm). I usually always have chard,
kale, chives, and catnip in this area, but have also had success with tomatoes
and pickling cucumbers.

The
tomatoes were quite acceptably productive, although probably a bit less than
they would have been in sunnier locations.
I staked them and they ended up growing almost a couple of feet higher
than the gutters – the pic below was taken standing on step ladder close to gutter
level. I eventually ended up with tomatoes resting
on the gutter guards!

Pickling
cukes did quite well and I think the bee-attracting catnip nearby may have
helped them along.

Bush beans
have done well in this area. Multiple
attempts with peppers failed (as I expected they would). Oddly, lettuce and spinach production was a
bit of a disappointment and I’m not sure why.

I’ve never
considered trying potatoes in that area but might try that this year.