"This is how sauerkraut is made in our home in Russia. It only takes 5 days and keeps well in the refrigerator. Serve it with some mild-tasting oil and chopped onion. Sometimes cranberries and caraway seeds are added for additional flavor."
Mix cabbage and carrots in a large ceramic or glass jar at least 1 gallon in volume.
Stir salt into spring water in a large bowl until dissolved; pour over cabbage mixture which should be completely submerged. Use an inverted small saucer to keep pressure on cabbage to keep it submerged in the liquid.
Cover container with a clean kitchen towel. Poking holes through the cabbage mixture to the bottom of the container with the handle of a wooden spoon to help gas escape once a day, keep on counter at room temperature for 3 days.
Pour a small amount of the liquid from the container into a small bowl; stir sugar into the liquid until dissolved. Return the liquid to the container.
Cover container, again assuring the vegetables are submerged in liquid. Keep on counter for 2 days more, again poking holes into the mixture to help trapped gasses escape daily.
Transfer vegetables and liquid to jars, seal, and refrigerate between uses.