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).
Place all ingredients in a medium mixing bowl and smash together with the back of a spoon. Taste test it by adding a small amount to a piece of plain bread or cracker. Adjust seasoning as desired and do another taste test. To store, form into a log using plastic wrap and store in the freezer until ready to use.
If you need to quickly bring cold butter to room temperature, cut it into 1" pieces and place evenly on a dinner plate. Cook in the microwave in 30 second increments at 20% power. The butter should be soft to the touch but not runny.