In a medium saucepan, combine the apple cider vinegar, water, honey, red pepper flakes, salt, and black pepper. Heat over medium heat until the mixture begins to simmer, stirring occasionally to dissolve the honey.
Once simmering, add the sliced garlic and optional mustard and coriander seeds. Remove from heat and let the mixture cool for about 10 minutes.
Place the sliced carrots in a clean glass jar or container. Pour the cooled pickling liquid over the carrots, ensuring they are fully submerged.
Seal the jar tightly and refrigerate for at least 24 hours before serving to allow the flavors to meld. For best results, let them sit for 3-5 days.
Serve as a tangy side dish, topping for sandwiches, or a zesty addition to salads.