Peel and cut the carrots into sticks about the size of your baby finger. Bring a saucepan of water to a boil and drop the carrots in; cook for about a minute, then drain them and run under cool water to stop them from cooking. Drain well.
In the same pot, bring the remaining ingredients to a boil, then reduce the heat and simmer for a minute. The sugar and salt should be completely dissolved.
Pack the carrot sticks into a jar or jars, and pour the brine overtop, tucking in the slices of ginger too. Let them cool, then store in the fridge for up to a month. They should be ready to eat in a day or two, but will be much better after a week.