Bring a medium-sized non-reactive pot of lightly salted water to a boil. When the water boils, add the carrot sticks and simmer for 1 minute. Pour the carrots into a colander and rinse under cold water. Drain thoroughly.
In the same pot, combine 1 ¼ cups water with the apple cider vinegar, granulated sugar, garlic cloves, fennel seeds, mustard seeds, bay leaf, and red chili flakes (or Aleppo pepper). Bring the mixture to a boil, then reduce the heat and simmer for 2 minutes.
Remove the pot from heat and add the carrot sticks to the pickling liquid. Allow the mixture to cool to room temperature. Transfer the carrots and liquid into jars and refrigerate.
Serve the pickled carrots with your favorite dip.