edible perennials in containers, NYC backyard

Hey all,
I have been going around in circles on the internet trying to find cold-hardy, shade-tolerant, edible perennials whose roots will survive overwinter - in containers - in my concrete-paved, tree-lined NYC backyard (zone 6b.) Any suggestions? Also anything that I might be able to get started planting either now or in the fall?

I'm more than happy to do the research (if you have any links or books specific to this region or those needs) but I keep going around in circles online as it is hard to find plants that check off all the boxes.

Dwarf hardy fruit trees,  chives, strawberries..   maybe chinese yam if you have room for climbers.    Sea kale might be another, not sure about containers as I'm just trying it for the first time.   What about sorrel, or edible hosta.  Some of it is going to be specific to  size of container, if you can cover well,  how much wind protection it gets from drying out, etc.   Gooseberries do well in shade if you are allowed to have them.  

Thanks!

I should add that the yard is fenced in on all sides by high walls thus there is no wind factor to take into account but there are plenty of climbing vine opportunities. I can completely control the container size and covering up of plants overwinter.

I'd experiment then!  Find plants that look like they meet 2 or 3 of your criteria and start there,  they may surprise you.   Microclimates count for a lot and if you have some wind protection and covering,  things might do better than expected.  

I lived in lower Manhanttan...coukd have had lettuce beds on the roof, didn't think of it at the time.

Sorrel
Skirret
Perennial wild cabbage
Tree collard
Ramps
Turkish rocket
Caucasian spinach
Sea kale

And maybe rhubarb. I would plant as many varieties as possible, keep the good ones and replace the bad ones with shade tolerant annuals like herbs, collards and large leaf silverbeet like the "fordhook giant" variety. I have two perennial pot gardens in a major city. My method is to fill the pot 80% with free draining soil and top with compost (sifted if i'm direct seeding). When you grow plants in the shade you need high quality compost or worm castings, as the lack of light slows growth and makes plants susceptible to pests and disease.

Raspberries, Jerusalem Artichoke. Just keep the latter in it's own container because it spreads like wildfire.

Blueberries should be OK. I’m thinking about trying grapes.

Currants will grow in shade - black, red and white. I'll second rhubarb, also Jerusalem artichokes, buckshorn plantain, mint.  Oh, and hardy fuschias grow in shade and have edible berries.  Apparently fiddle head ferns, but I haven't grown them myself.
Miners lettuce and lambs lettuce are reliably self seeding annuals so they're a bit like having more perennials
Looking forward to updates!

Ben Schiavi wrote:And maybe rhubarb.  

My friend grows rhubarb in containers in a similar urban setting, with great success. Deep but not very wide container, like you would for an orange tree on a patio.

I'm experimenting with Egyptian Walking Onions in hanging baskets.  So far I have five that are about 4" tall and 12 more that I just planted yesterday.  

I only have 3 hanging pots available so I might try some pots in my laundry room.

I am sure I will need to harvest often and replant.

I don't think they will do their walking in the hanging baskets so I plan to harvest the bulbis and plant those.

The deer decided to eat my onions so this is why I am experimenting.

I'm a big believer in polycultures, even in containers
Here's a combo of shade tolerant perennial herbs and vegetables I grew in a tub that is 70 cm long, 55 cm wide and 30 cm high:

Good King Henry (Chenopodium Bonus-Henricus), Welsh onion (Allium fistulosum), Sorrel (Rumex spp), Purple plantain (Plantago spp.), Lemon balm (Melissa officinalis), Salad burnet (Sanquisorba minor)

It looks quite pretty too!