Ukrainian Style Saurekraut

This is my childhood's sauerkraut. The big jar of fermenting cabbage with a precariously balanced stack of smaller jars weighing it down is pretty much a staple in any Ukrainian grandmother's kitchen, and I have very fond memories of sneaking samples from the giant jars (regardless of how close to done they were) while my grandmother was busy elsewhere.

This version is dryer, crispier and generally milder-tasting than the German-style sauerkraut you generally find at the store. While it's incredibly delicious raw, it's also the main ingredient in the tasty but underrated sour cabbage soup (Sour Schi in Russian, or the similar Ukrainian and Polish Kapusniak), and also makes for a nice stewed cabbage side dish, both of which I'll get to later.I posted a more detailed version of this recipe and process here a few years ago.

Supplies
You really don't need any special supplies to make sauerkraut. A fermentation crock is nice, but it's really not necessary. You can use a widemouth jar, a large glass or ceramic bowl, a lead-free crock or a food-grade bucket. Whatever you you end up using, make sure you can fit something inside to weigh down the cabbage. You can get food-grade buckets for free at the bakery section of any major grocery store if you ask nicely, and these fit a dinner plate nicely. If you have an Ace Hardware nearby, they have the best prices on Ohio Stoneware crocks.

Ingredients:
Cabbage
Carrots
Coarse Sea Salt or Kosher Salt
Fresh Cranberries (optional)

Process:

1. Shred your cabbage and carrots. I usually use my mandoline to get super thin slices, but it's really a matter of personal preference. 
2. Add salt to shredded cabbage and carrot mix. Salting kraut is an art, so there's no solid answer for how much salt to add, but the general rule of thumb is 3 tablespoons of salt per 5 pounds of cabbage. I use a tablespoon per cabbage, which probably amounts about the same thing. Eventually you'll be able to tell if you've added enough salt just by tasting the brine, but in the meantime use 3tbsp per 5lb of cabbage.
3. Thoroughly mix cabbage and salt with your hands, thoroughly crushing it so it releases all the water it holds. You'll know you're finished when the cabbage is limp and no longer has any crunch. 
4. Add cranberries, if using, and transfer cabbage to the container it will be fermenting in, packing it in as tightly as you can. Use your weight to press down the cabbage down as low as it will go. There will be an awful lot of brine, sometimes overflowing your container. As the cabbage ferments, it will release more water so you'll be able to compress the cabbage even further. The more liquids you squeeze out of the cabbage, the crunchier the end result will be. Large batches are easy to weigh down, since you can stack any number of jars filled with water on top. For smaller containers you'll have to get creative, using bottles and smaller jars.
5. Leave your sauerkraut to ferment at room temperature. Depending on your climate, the kraut will be ready in 1-2 weeks, sometimes as early as 3 or 4 days. Once the mixture begins smelling sour, you can sample the kraut to test for readiness. Once you feel it's ready, you can move it to the fridge where it will keep pretty much forever.

Troubleshooting:

•  If at any point during the fermentation process you feel your kraut is too salty, replace some of the brine with fresh water. 
• Scum will occasionally form on top of your brine. This is normal, and you can simply skim it off and discard.
• There should always be a layer of liquid above the layer of cabbage. If there isn't, you're probably not compressing it enough.
•  A cooler climate will yield longer fermentation times, but a hot one increases your chances for icky, soggy cabbage.