Begin by slicing the banana peppers into ¼ inch rings, discarding the stems. If preferred, you may remove the cores, though it’s not necessary. Pack the pepper slices tightly into clean, sterilized 1-pint jars or a larger quart jar.
In a large pot, combine the white vinegar, water, honey, pickling salt, smashed garlic, dried oregano, dried basil, and black peppercorns.
Bring the mixture to a rapid boil, then remove it from the heat.
Allow the brine to cool slightly before pouring it over the banana pepper slices in the jars. Ensure the peppers are fully submerged. Seal the jars with their lids.
For the best flavor, refrigerate the jars for 24 hours before consuming, although they are ready to eat immediately if desired.