Place the carrot sticks, ginger, and garlic in a sterilized 1-pint jar.

Heat a small saucepan over medium; add coriander and cumin seed and toast the spices for a minute or two until they’re fragrant. Take the pan off the heat for a minute to cool. Add vinegar, water, sugar, salt, and cinnamon stick; bring to a boil and simmer until sugar and salt are dissolved. Pour the brine over the carrots (leaving ½ inch of headspace). Cover jar with a new lid and band. Let cool to room temperature, then refrigerate for at least 2 days to develop flavor. Keep for up to 1 month, refrigerated.