First - beans are NOT low carb. Half a cup of white beans, cooked, has about 28 grams of carbs.
Now,
Get some olive oil heating in your pot, chop up an onion or two, add to pot, stir it a bit. While that is going, chop or slice up carrots (stir the pot) and celery. Add to pot, stir. Grate in some garlic, as much as you like. Stir. Chop your cabbage (stir the pot several times while doing that). Add to pot and stir. Add water or beef or chicken stock to cover by an inch or two. Add your soaked beans, or canned beans (I like navy beans, but just about any other than black will work - black too, if you don't mind a funny color). If using canned, go ahead and add your salt and pepper now, otherwise wait 'til the beans are cooked, then season. I like dill and thyme in my cabbage soup. Also a touch of tobasco and some cider vinegar. A bottle of beer into it doesn't hurt either.
You could also use split peas or lentils.
Also, look up borscht recipes - real peasant borscht is basically cabbage and beat soup, nice and chunky, not the thin blended and strained stuff.