I make quite homemade sauerkraut often and I've never seen a recipe like this. Real sauerkraut has two ingredients: cabbage and salt. No vinegar is used. It's also about the easiest thing in the world to make if you have a little patience. This is the recipe I use to make a little under a gallon of homemade kraut:
4 heads cabbage, green or red
4-6 tablespoons kosher or pickling salt
You'll need a one gallon container. The ideal vessel to use is a ceramic crock. This
is similar to the one I have. You'll also need a plate that fits inside the crock.
Core and shred the cabbage, one head at a time. As you finish shredding each head, put it into a large bowl and sprinkle it with 1 to 1-1/2 tablespoons salt. I like it less salty, so I stick to the low end.
Then you want to squish (or massage, as my wife says) the cabbage in your hands until it releases quite a bit of water. This will take about 5 minutes. Then pack it tightly into the crock. Repeat with each head of cabbage.
When you are finished, use your fist to compress the cabbage in the crock as tightly as possible. You want to get out any trapped air. Ideally, there should be enough liquid that the cabbage will be entirely submerged. This is important. If it isn't submerged, top it off with enough water so it's covered by about a half inch to three quarters of an inch.
Put a plate on top of the cabbage, and then put a weight on top of that to hold the plate down. I use a quart size mason jar full of beans. Put a towel over the top of the crock to keep out dust, etc.
Put the crock in a dark, cool place and leave it alone to ferment for at least 10-14 days. At this point, it's usually at the stage of sourness I like. But you can go as long as 6 weeks. Check it a couple of times a week. If you've done everything right, you shouldn't see any mold on the surface, but if you do, just skim it off with a spoon.
Now at this point you can either can it or just put it in the fridge and use it as is. It will keep for at least a month or more. Maybe longer. Though I've never found out because it never lasts that long in my house.
I like it raw myself, so I don't can it.
If you decide to can it, you want to cook the kraut for 20-30 minutes at a low simmer. Pack it into sterilized mason jars, leaving a half inch of head space. Make sure to pack tightly so there are no air bubbles. Then process the jars for 15-20 minutes in a boiling water bath.