Cut carrots into sticks or if you’d like, coins.
Pick a quart jar that has ‘shoulders’ to help you keep your vegetables below the brine. Small mouth quarts have shoulders, and some wide mouths do but not all.
In the bottom of the jar, add mustard seeds, peppercorns, coriander seeds and fresh garlic cloves.
Stuff carrots into the jar.
Use a horseradish or grape leaf or one of the other ideas to keep them submerged - this is very important to keep it from going moldy (see notes).
Put a lid on and don't crank it on unless your fermentation weight requires that. If you can leave the lid loose you won't need to burp it. Let them sit on counter, on a baking sheet or plate in case they overflow, for 4-7 days.
Once the brine is cloudy you know that fermentation is doing its thing! Make sure pickles stay submerged this whole time. You can start tasting them on day 4; only leave longer if you like them really sour. We err on the side on less sour since we are storing them for up to a year.
Tighten the lid,, move to fridge or cool room and they keep 6-12 months. Once we want to eat them, the fermentation weight comes out and doesn't need to go back in.