Because of the chemical change is the nutrition changed?
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I would! Sounds like a tasty variation. I make that soup often, especially this time of year. In fact, here's my version https://food52.com/recipes..., although I change it up a bit every time I make it.
I always keep it on hand in the freezer for a revamp after a big cheat on my lifestyle change. I found sauerkraut on sale and have a bunch i wondered. I am gonna soak some of the sodium out. I will definitely checkout your recipe and let you know how it turns out!
It is up to your taste. Sauerkraut is a bit acidic, but you can always rinse it. I still prefer fresh cabbage in soup though. If you don't want to wait the time for the cabbage to soften, try a variety of soft leaf Asian cabbage.
This is a great answer. I did rinse it and so far so good on the cooking. I actually like the crispness of cabbage.