Wearing gloves to protect your skin from irritation, slice off the stems of banana peppers and remove any large membrane with a paring knife. Cut peppers into thin rounds and divide between 2 sterilized pint jars or 1 quart jar.
In a medium saucepan, combine vinegar, water, salt and honey; cook and stir over medium heat just until boiling. Remove from heat and carefully pour hot liquid over peppers, leaving ½-inch of space at the top. With the back of a spoon, press peppers down so they are below the liquid. Let cool to room temperature and then screw on the lid and refrigerate overnight. Enjoy as early as the next day and for up to 1 month.