Prepare a boiling water bath canner and four pint jars.
Shred the kohlrabi using the grating disc of your food processor or a box grater. You should have about ten cups of grated kohlrabi.
In a large, non-reactive pot, combine the kohlrabi, apple cider vinegar, garlic, salt, and pepper. Set over high heat and bring the contents of the pot to a boil. Once the liquid boils, cook for 3-4 minutes, until the kohlrabi slumps a little and release some of its liquid.
Using tongs, pack the kohlrabi into the prepared jars and ladle the liquid over to cover, leaving 1/2 inch headspace. Use a chopstick or plastic bubbling tool to remove any trapped air bubbles, and add more liquid, if necessary.
Wipe the rims, apply the lids and rings, and process in a boiling water bath canner for 15 minutes.
When time is up, remove the jars from the canner and set them on a folded kitchen towel to cool.