If Canning, prepare a water bath canner, jars, lids, and bands before beginning. The canner should be preheated for hot pack, which means at a gentle simmer (around 180 degrees F).
Wash and clean the brussels sprouts. Time the stem ends and remove any outer leaves. The sprouts should be small, tight heads. Cut any large sprouts in half.
Bring a pot of water to a boil and blanch the sprouts for about 4 minutes. Remove with a slotted spoon and pack into jars, leaving 1/2 inch headspace. Discard cooking water.
Add dry spices to each jar (but not vinegar, water, and salt).
Add the brine ingredients to a pot, including vinegar, water, and salt. Bring it to a hard boil, stirring to dissolve the salt.
Pour the boiling brine over the brussels sprouts in jars, maintaining 1/2 inch headspace. De-bubble jars, adjust headspace and cap with 2-part lids
If canning, process in a water bath canner for 10 minutes, adjusting for altitude (see notes).
Remove the jars from the canner to cool on a towel on the counter. After 12-24 hours, check seals and store any unsealed jars in the refrigerator for immediate use. Properly sealed jars should maintain quality on the pantry shelf for 12-18 months.
I'd suggest waiting for at least 1 week before eating the brussels, to allow time for them to properly pickle and for the flavors to infuse.