One sauerkraut recipe you can store in a quart jar is the small batch sauerkraut from Serious Eats. The recipe includes just three ingredients and takes 10 minutes of active preparation with two weeks of fermenting.
To prepare the recipe, find one small cabbage weighing approximately 2 pounds, and remove the core. Cut the cabbage in half before cutting it into fine shreds using a sharp knife. Place the shreds in a large mixing bowl, sprinkling them with 1 tablespoon sea salt. Use a potato masher or your hands to knead the salt into the cabbage, squeezing out the moisture. Once the amount of cabbage appears to have been reduced by 50 percent, sprinkle in 1 teaspoon caraway seeds, working them into the cabbage.
Add a layer of cabbage to the quart jar, compressing it before adding the next layer. Continue until you've fit all the cabbage into the jar. Press the entire batch of cabbage firmly into the jar until the liquid seeps to the top, and loosely place the cap on the jar. Let the jar rest in a cool, dark area, checking every few days to remove any growth from the top of the liquid and push down any cabbage that floats up.
After two weeks, taste the sauerkraut. Place it in the fridge if you like the flavor, or let it continue to ferment for a stronger sauerkraut.