Gently transfer the leeks to a quart-size jar while attempting to keep most of the inner rings intact. Combine the water, sea salt, and thyme in a separate jar or bowl until the salt dissolves. Pour the sea salt brine over the leeks until submerged. Weighing down the leeks below the brine is optional but not necessary if checked regularly.
Leave to ferment, away from direct sunlight, for at least 3 weeks until leeks are tender.
Make certain to release any CO2 buildup in the first week by quickly opening and closing the lid.
Taste and when fermentation is to your liking, move to long-term storage (i.e., refrigerator, basement, root cellar).