I've neglected to include amounts in the ingredients because this recipe is totally adaptable-base your amounts on the number of jars you have, or the amount you feel like making! One note, though: ginger can become overpowering kind of quickly. One possible ratio is 1Tbsp ginger to every 4 cups of carrots. I often simply include a couple thin slices of ginger root to every pint size jar.
Sterilize your jars: I do this by placing my jars in a clean sink and pouring boiling water over them. You could also fill the sink with boiling water, and use a tongs to submerge each jar. When they are cool enough, remove jars to the counter. They will not stay medical-grade sterile on your kitchen counter, but this step will still serve to rid them of a lot of potential bad bacteria.
Wash, peel and slice your carrots to your desired size. Wash, peel and slice or grate your ginger root as well.
Place your carrot sticks and ginger in your jars. They should be cut to a length that will allow the brine to fully cover them without spilling out of the jars.
Make your brine: I do this by zeroing my kitchen scale with a large liquid measuring cup on it, then adding water to the measuring cup. Take the weight of your water in grams, then calculate 5% of that weight, in grams (for example: 500g water x .05= 25g)
Your calculated 5% figure is the amount of salt you should add, in grams. Add your calcuated amount of kosher salt, then mix until the salt dissolves.
Pour the brine over the top of the carrots, until they are fully submerged. I find that carrots do an okay job staying under the brine, but you can also use fermenting weights to accomplish this.
Leave the carrots at room temperature to ferment. You can cover them with a valved lid designed specifically for fermentation, or you can just partially twist on the regular jar lid--if you do this, un-twist it every day to make sure any built up gases can escape.
The length of fermentation time needed depends on a couple of factors, especially the temperature of your kitchen. In the summer, I let my carrots ferment for 3 days. In the winter, it could be more like 5 or more. After a couple days, you should start seeing bubbles rising in the jar: the evidence of fermentation. After 3 days, you can start tasting your carrots, and stop fermentation when they've reached your desired sourness. ("Sour" doesn't seem like the right word--I think you'll see what I mean)
When your carrots have finished fermenting, close jar firmly with a lid and transfer to the fridge.
Enjoy! These make a great side to all sorts of dishes, or a snack on their own.