Fill your largest pot with water. Sterilize your jars by submerging them (while the water is still cold - or they might break) and turn the heat on high. Bring to a boil. The jars need to boil for at least ten minutes, but keep them in the water till you're ready to fill them. You want to keep them warm because you will be processing them in boiling water again, and if they have time to cool off before returned to boiling water, they may break. Warm the lids in a small pot of simmering water (not boiling) over medium-low heat. Use the tongs to remove jars and lids from water.

In another medium-large pot, combine vinegar, salt and 4.5 cups of water. Bring to a boil and stir to dissolve salt.

Meanwhile, spoon 1 tbsp pickling spice into each jar. Divide the garlic and dill among jars (about 2-3 sprigs of dill per jar). Pack the carrots snugly into the jars. Ladle the hot brine into the jars, leaving 1/2 inch of headspace. Place a warm lid on top, and secure with a screwband to just-sealed (not too tight - air needs to escape). Using the rubber-banded tongs, lower the jars gently into the boiling water. Process for 7 minutes, timed from when the water returns to a boil. *

Note that more is not better here - if you over-process them you will have soggy carrot pickles instead of crunchy ones.

Remove from water and allow to cool, undisturbed, for 24 hours. The jars have sealed properly if the lids are rigid and slightly indented. You might hear a "pop!" when it seals. The lid should not bounce back when you gently press it. If it bounces back and makes a clicking sound when pressed, the seal is not good. Keep any failed seal jars in the fridge for 2 weeks. All sealed jars will keep in a dark, cool place for up to 1 year.