Fall Potatoes

I have never had success with potatoes. This past year was no exception. I planted some new potatoes in the spring, they thrived and made small bushes. Then they promptly died back to nothing, mid summer before maturing.
Now, here in the middle of October those abandoned plants have decided to come back. Since I obviously don't know what I'm doing I have come here for some advice.
What should I do with these plants? Ignore them until they go away? Dig them up? Baby them?
Has anyone had experience with fall potatoes?

Hi Kevin, I had some potatoes do the same thing this year, so I am mulching them with over one feet of leaves/straw and letting them winter in the ground.  I will dig them as I need to use them.  I'm in Kentucky, USA zone 6b.  I do not know your climate, though, so it might be difficult for others to recommend.  Do you mind sharing more your general climate area in zone 7? Do you get frosts? freezes?

Thanks! I do get occasional frost (last night in fact was the first) but NC Piedmont doesn't really get a lot of freezing. At least not relative to other parts of the country.
I have aged wood chips, do you think that would be too heavy? I don't think any neighbors have started raking leaves yet.

I think the aged chips would make a nice insulator.

I'm in zone 6b.

I have a "perennial" potato patch at my in-laws house from where I grew potatoes in 2019 and didn't find all the potatoes when digging that summer.

I'm experimenting with fall planting some yellow potatoes that sprouted in my pantry. I intercropped with onions and garlic in a small bed in the middle of our young orchard and mulched heavily with hay (yes, I know, hay seeds will sprout, but if you keep mulch on all the time you really don't have to worry about weeds much.) I'm planning to do the same with the red potatoes that are also sprouting (except just intercrop with garlic bulbils since I'm out of onion sets and garlic cloves). I think it might work better with storage potatoes like Kennebecs, but it's an experiment and I want to get more Kennebecs for seed when planting the normal way in the spring when I am fairly confident of getting some return on my investment. I know I'll get garlic at least from this fall planting!

Different potatoes have different harvest times. Early, mid, late. Early potatoes rush to grow and tuberize then die back. Potatoes ready to harvest in a short time.
Of you want a big harvest of bigger potatoes you need a variety that will do that.

https://www.motherearthnews.com/organic-gardening/growing-potatoes-early-midseason-and-late-varieties-zmaz08djzgoe/

General reminder, store potatoes for eating can carry disease. It is best to plant potatoes sold as seed potatoes which have been specially screened for disease.

I normally grow two potato crops (June and December) each year here in upstate South Carolina.  The spring crop plants grow from late March into June when the plants do dormant in the summer heat.  Then any tubers left unharvested will start growing again in September and continue until frost kills back the top growth.  When fall frosts threaten, I cover the plants with a heavy grade of frost cloth to extend the growing season and get them through the frosty nights undamaged.  I can usually keep them growing into mid to late December before a severe enough frost gets through the frost cloth to kill the plants, at which point I harvest the tubers, leaving some to start the spring crop.  Because of the short day length, the December crop won’t be as large as the June crop, but fresh potatoes for Christmas dinner are always welcome.  Since the growing season for fall potatoes is fairly short, early maturing potato cultivars such as Red Norland work the best.