Add the vinegar, water, kombu, garlic, sugar and salt to a medium saucepan and bring to a boil over medium heat, stirring to ensure the sugar and salt have dissolved. Add the carrots and cook for an additional 2 minutes (the liquid may not come back up to a boil, which is fine, the goal is to just slightly soften them).
Transfer to a quart sized canning jar and allow to come to room temperature. Seal with a lid and transfer to the refrigerator. Enjoy within two months.
I sliced the carrots using the 3mm setting on my Oxo mandoline (which translates to about .12 inches).