If you are water bath canning these pickled carrots, prepare your water bath canner, mason jars, and lids. Wash your jars and lids. Sterilize your jars in a large pot filled with water. Bring the water to almost a simmer over medium heat. Keep the jars in the simmering water until you are ready to fill them. Use a jar lifter to remove them from the water when you are ready to fill them, dumping the hot water back into the pot when you remove each jar from the water. Right before you are ready to can, put your lids in a small pot or bowl with hot, but not boiling water. Put some additional white vinegar in a small bowl alongside a clean washcloth or paper towel. Keep the water in your canning pot at a simmer while you fill your jars.
Peel carrots and slice them to your preference. The thinner they are, the quicker they will pickle. If you keep them long carrot sticks, ensure they will fit into your jar when lidded. A standard pint, wide-mouth mason jar is 4 5/8" tall. If you use a wide-mouth mason jar, make sure the carrots are no longer than 4" to get the appropriate head space.
Slice garlic cloves into 3-4 slices.
Place carrots in a wide-mouth, pint mason jar.
Make the pickle brine by combining vinegar, water, sugar, salt, bay leaf, peppercorns, mustard seed, sliced garlic, and cumin seed in a small saucepan and bring it to a boil.
Once the vinegar water brine comes to a boil, remove it from the stove and pour the brine over the carrots. Make sure to add all the seeds, spices, and garlic to the jars with the carrots. If you use multiple jars, divide the spices and herbs among the jars. Leave 1/2" headspace.
Remove any air bubbles.
Wipe the rim with straight vinegar and center the lid on the jar.
Screw on the band until it is fingertip-tight. Repeat with the remaining jars.
When all your jars are in your canner with at least 2 inches of water over top, bring your canner to a boil.
Once boiling, process your pint jars for 15 minutes, adjusted for altitude.
At the end of 15 minutes, turn off the heat, remove the lid, and let the jars sit for 5 minutes.
After 5 minutes, remove them from the water and place them where they can sit undisturbed for 24 hours.
Refrigerate any jars whose lids don't seal.