In a saucepan, combine apple cider vinegar, honey, red pepper flakes, salt, black peppercorns, and garlic. Bring to a simmer over medium heat while stirring occasionally to dissolve the honey completely.
Once the mixture is simmering, add the carrot sticks into the brine. Stir gently to ensure all the carrots are well coated.
Remove the saucepan from heat and let it cool for about 10 minutes.
Transfer the carrots along with the pickling liquid into a clean jar or airtight container.
Refrigerate your jarred carrots for at least 24 hours before serving.