Using a mandoline, slice the carrots into 1⁄8-inch-thick planks. Run your knife lengthwise through the planks, cutting into matchsticks. Put the carrots, red pepper flakes, and bay leaf into a 1-quart mason jar.
In a saucepan over medium-high heat, combine the carrot greens, vinegar, water, salt, sugar, fish sauce, carrot seeds, and peppercorns and bring to a boil. Then, remove from the heat and let the pickling liquid cool a bit (it should still be warm).
Pour the pickling liquid over the carrots. Allow to cool to room temperature, put the lid on the jar, and transfer to the refrigerator for 48 hours to pickle. The pickle will keep, refrigerated, for up to 3 months.