Start by taking your mason jars of choice (we used the smallest glass variety) and submerge each glass in a bath of boiling water (with lids and tops in separately) to clean and bring them up to temperature (approximately 5-10 minutes). Using silicon-tipped tongs, grab a mason jar from the water, carefully drain the rest of the water back into the pot, and place the glass on a wire rack or towel. This prevents the jars from cracking when hot liquids are added later.
Wash and chop all veggies you'll be pickling (our first four ingredients). Once the jars have cooled to the touch (about 3-5 minutes), layer your jars with the filling, starting with garlic, then onions, and then cabbage.
In a medium sauce pot, combine the remaining ingredients for the pickling brine over low heat, slowly simmering and stirring until the sugar has incorporated into the other ingredients (about 3-5 minutes).
Assembly time! With a wide-mouthed funnel over the first filled mason jar, carefully pour the pickling liquid until it reaches about 1-2 millimeters from the top, and repeat this process with all remaining jars. You should have enough liquid using the small jars for this recipe (they're almost 1 cup of liquid each) or a couple of larger, total volume equivalent-sized versions.
Wipe the top and side ridges on the jars before capping off and putting on the lids to ensure a clean seal. Then return them to the hot water bath for 3-5 minutes, or until the tops of the mason jars stay tight and don't bounce when pressed on. They usually come with a built-in center that you can "pop" or press up and down when they're not sealed, and it stays tight or depressed when it's sealed as a visible reminder of that fact. After the bath, carefully take the jars out with the silicone tongs and let them cool down on a wire rack or towel, allowing them to rest and ferment for 3-5 days before opening. If sealed properly, these will last a year in the pantry without refrigeration. If not sealed, they last in the fridge for 1-2 months.