I've tried fermenting vegetables, and so far the one that has worked best is cabbage, aka sauerkraut. There are much better sites that describe the process than what I can provide; see for example Nourishing Treasures (the link is to the final report, but there are numerous other posts on the experiment linked from that page; the whole package is very detailed).
Here's what I have experienced: First, my house is normally somewhat warmer than the typical upper 60s-lower 70s temperature range suggested for kraut fermentation. In the summer, my house is usually around 80. Because of this, I have never let a batch go for 28 days. I don't let it go too much past when the CO2 action fades, although as the Nourishing Treasures posts note, that may be ending things too soon (see also this post by the same author, Lea Harris: Fermentation Mistakes. Some sites warn that spoilage may occur at higher temps, but I have never had a problem--although last summer, a batch seemed to be through its CO2 cycle within a week.
Two pounds of cabbage plus one tablespoon of canning salt is all that's needed. Two pounds is around one normal-sized head; when chopped and put into the jar initially, it fills it.
To get things ready to ferment, part of the process is mixing the salt in with the chopped cabbage, which begins to liberate water, and massaging/crushing/stomping the mixture to bruise the leaves. This in turn liberates more water from the leaves. I have often massaged the cabbage a lot in a bowl, then crushed it with my fist once it's in the jar.
Things will rapidly start to get a little foamy. The two pounds of cabbage, when crushed/compressed, fills the jar about halfway. I took a piece of thin plastic and cut it in the shape of the jar, below the shoulder, and use that to hold down the cabbage leaves. In the picture below, you can see some glass weights holding it down; those are Pickle Pebbles. I have the wide mouth size. I stacked three on top of the plastic. I got the plastic itself from a pack of bacon (washed, of course).
This time I did a larger batch. Two pounds is okay, but more is desirable. A number of companies sell airlock fermentation crocks; as noted in various places they are fairly expensive and some are available in very large sizes. One of the factors to consider is that, while it is not necessary to fill the crock, there has to be enough cabbage to generate enough CO2 to fill the airspace. Filling a vessel all the way is a bad idea, because it heaves a bit as it ferments, but if it is only 25% full, that might be a problem.
I put about six pounds into the crock and another two pounds into the mason jar (I wanted a visual check of what was happening). The crock was a 5 liter model from Stone Creek Trading (I like the glass weights). Although cost per volume drops dramatically with larger crocks, I realized that I'm not--for now--likely to want to make more at any one time than what the 5 liter model will hold.
The foaming action died down after about 10 days and I let it go another 10. At that time I noticed a little mold starting to form at the edge of the water in the gutter at the top of the crock. I opened it up and ended up with a little over a gallon, including what was in the mason jar and what was in the crock.
There was no mold inside the vessel; what you see above is some petrified foam. There's also a lot of water (both in the mason jar above and the crock); I added some when my stomping efforts didn't get enough fluid to cover the leaves initially (I used a 3 tablespoons of salt per gallon mixture of water, suggested by NW Edible).
I tested the pH of the mixture; it's a little difficult to do with red cabbage, because the red stains the test strip. But it seemed to be in the 3.5-4.0 range, which is good enough for me. The Nourishing Treasures trial found 3.0-3.5 after 28 days.
I have noticed that the kraut gets tangier as it sits in the refrigerator; it is no longer submerged (except at the bottom of the vessel), and fermentation slows way down--but to some degree, it may continue. Storage at room temperature is apparently okay for a relatively short time; that's why this food preservation technique came into use (although as I noted above, my room temperature is not the same as what would have been typical in Europe in the fall and winter, to say the least).
