Wash and dry duck eggs, then roll duck eggs in a bowl of clear, high-ABV (>50% ABV) spirit like baijiu or vodka (I used Mei Gui Lu, which you can buy in some Chinese grocery stores. Shaoxing and other low-alcohol Chinese cooking wines are NOT an appropriate substitute).
Nestle eggs carefully in brining vessel.
Bring the water to a boil, then dissolve 1½ cups of kosher salt in the water. Let cool and pour over the duck eggs. The brine should be extremely salty, even a bit bitter, and should completely cover the eggs. Seal jar and store in a cool place out of the sun. If you are using a Chinese pickle jar, you'll need to make sure the moat is always full of water, so check it every week or so.
After a month, eggs can be moved out of the brine and stored in the fridge. Pro tip: Hang on to the cartons when you begin your brine so that you can put the eggs back in the cartons for long-term storage.