However, as you can just make out in the picture, in our haste to bring in all the squash, we broke off the stems. This is bad, because multiple sources—from nurseries to state extension offices to Organic Gardening magazine—say that squash won't keep well if the stem is removed. Breaking off the stem, sources indicate, exposes the flesh of the squash to microorganisms that cause it to rot. So when I noticed that all five of our squash had been damaged in this way, I feared that we were going to have to eat them all up in a hurry, or else figure out some way to make room for a lot of squash puree in our freezer.
Fortunately, Brian reassured me that he's picked squash this way in the past, and they still keep for several weeks at least. Maybe not all winter, but then, given how many things we like to make with butternut squash, it's unlikely they'd last that long anyway. However, he also mentioned that if I was concerned about them, it might be possible to patch the damaged ends somehow. A quick search turned up a comment on the Farmer's Almanac website saying that if the stem breaks off a pumpkin, you can disinfect the "wound" with a bleach solution and then seal it up with a dab of petroleum jelly. I didn't have these things handy, however, so instead I selected a couple of the smaller squash (the two that looked most severely damaged), wiped them down with hydrogen peroxide, and then sealed up the wound with melted wax. I had some leftover Hanukkah candles from last year, and I knew from experience that they drip like crazy, so I just lit one and held it over the damaged part of the squash, moving it from spot to spot until the entire breach in the flesh was covered. Since I used an orange candle, it doesn't even stand out that much.
We'll store the two wax-patched squash along with the three others and see whether they seem to keep any better than the ones that haven't been patched. If so, then we've learned a potentially useful trick for salvaging any squash that get damaged from future crops; if not, then as Thomas Edison said, we've discovered a way that doesn't work. But either way, we've learned to cut the stems in future, rather than pulling the squash right off the vine.