Wash and drain the banana peppers. Set out a mandolin slicer. Carefully slice the banana peppers into 1/8 inch rounds. *This is best done with mandolin slicer because it's fast and slices the peppers very evenly. However, you can also slice them with a chef’s knife if needed. Either way - BE CAREFUL!
Stuff the banana peppers in the jars, packing them down if needed so they all fit.
If using quart jars, place two garlic cloves in each jar, followed by ½ teaspoon of Italian seasoning and ½ teaspoon of celery seeds. If using pint jars, place one garlic clove in each jar with ¼ teaspoon of Italian seasoning and ¼ teaspoon of celery seeds.
Set a large pot over high heat. Add the vinegar, water, sugar, and kosher salt to the pot. Stir and bring the vinegar mixture to a boil. Once boiling, turn off the heat.
Ladle the hot pickling liquid into the jars. Fill them to the top, covering the peppers, but leave ½ inch of room at the very top of the jar. Screw the lids on tight.
If planning to keep in the refrigerator, allow the jars to cool to room temperature and then place in the refrigerator.
Either way, let the banana peppers pickle for at least 48 hours before serving.
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Notes
Following proper canning procedures, jars of pickled peppers will keep well for at least a year at room temperature. Whether you can or "quick pickle" them in the refrigerator, once opened, the banana peppers will stay good for up to 2-3 months or so in the fridge.