Add vinegar, water, sugar, and salt to a large saucepan set over high heat and bring to a simmer on the stovetop. Cook for 5 minutes, or until the sugar and salt have completely dissolved, then remove from heat.
While the brine simmers, divide the red pepper flakes, mustard seeds, black peppercorns, coriander, bay leaves, and garlic cloves between two pint jars.
Slice the Brussels sprouts in half and add them to the pint jars, removing any dirty or loose outer leaves. Small Brussels sprouts can be left whole.
Fill the pint jars with Brussels sprouts, then pour in the hot brine until it reaches ½ inch from the rim. The Brussels sprouts will soak up some pickling brine, so you may need to top it off again after a few minutes. Wipe rims clean, then seal with jar lids.
Fill a large pot or water bath canner with enough water to cover the jars and bring to a boil. Gently set the canning jars into the pot of boiling water. Process jars for ten minutes.
Remove the jars from the boiling water and set them on the counter to cool. After a few minutes, you should hear the jar lids make a popping sound as they seal. Store the jarred Brussels sprouts in your pantry for at least two weeks, then enjoy, and refrigerate after opening.
Notes
Rather than using a water bath, you can make these as refrigerator pickles by storing them in the refrigerator instead. When kept properly stored, pickled Brussels sprouts will keep for months.