Can potatoes overwinter and still be edible? Doubtful. Same goes with parsnips.

Can potatoes overwinter, grow, and produce edible tubers? Yes. Would I expect this to occur reliably? No.

Also, parsnips are not all that edible once they start to actively grow in springtime, but they will grow reliably and go to seed which can be harvested and planted to produce edible parsnips next year. Seeds will drop and make babies without human intervention as well (can be a nuisance). Salsify works pretty much the same way.

Potatoes that overwinter and grow here we call "volunteers". They are from potatoes that were missed when the hills were dug up during the previous harvest. We usually leave them be and dig as new potato "freebies" during high summer.

If you are into the guerrilla gardening thing, which is kind of a cool concept, think perennial vegetables for Minnesota such as Jerusalem artichoke (Helianthus tuberosus), Ostrich fern (fiddleheads), Egyptian Walking onions, horseradish, asparagus, ramps, lovage (Levisticum officinale - celery family), and perennial herbs. Shallots, multiplier (potato) onions, and garlic work kind of the same way but better to harvest and replant some every fall for next year's harvest.

Keep in mind many common "weeds" are edible as well (and fairly tasty).

Lots of good food to be had with little maintenance and effort if one keeps an open mind and has willing taste buds. :)

Have fun!
-Tom

We always let our parsnips overwinter and dig early in the Spring before they start to grow. Or dig late in the Fall. Seems their taste is improved by a frost. Just an idea to try.

I bought some yummy over-wintered parsnips at the St Paul market last week. They might have been dug and stored underground. Several of my parsnips survived even cultivation this spring and are growing again. No sign yet of seeds starting but I plan to save seeds from them. My old parsnip seed is too old now and I hope to get more.

As for potatoes, in mild winters you can get volunteers but it is not reliable. My mind has been on whether you could plant potatoes in fall in a high tunnel and when they would start growing in spring and when they would be harvestable. Good if you had more than one high tunnel. I have none so I wonder if they would survive to early volunteer in a low tunnel. Save storage space and give you a crop before the bugs hit!