Set a fine-mesh sieve over a deep bowl and line it with three layers of clean, damp cheesecloth, leaving room underneath for the whey.
Stir the sea salt into the milk kefir until evenly mixed.
Pour the salted kefir into the cloth-lined sieve.
Cover the kefir with the overhanging cloth, then cover the bowl.
Refrigerate the covered sieve and bowl at 4°C (40°F) or below for about 24 hours, until the cheese is thick enough to spread.
Check the bowl once or twice while it strains and pour off the whey before it reaches the bottom of the sieve.
Scrape the strained cheese into a bowl and stir until smooth.
Spread the labneh on a small plate with the back of a spoon, leaving shallow hollows.
Drizzle with the olive oil and sprinkle with the dried thyme.
Pour off the collected whey before it reaches the bottom of the sieve.
Expect about 200 g of cheese before adding the oil and thyme, enough for 4 small appetizer portions. The yield varies with the thickness of the kefir. If it is still too loose after 24 hours, keep straining in the refrigerator for up to 36 hours in total.
The Greek Yogurt Maker can replace the sieve and cloth: pour in the salted kefir and leave it in the fridge.
Storage and safety
Store the strained labneh in a clean, covered container at 4°C (40°F) or below and eat within 3 days of straining. If the kefir package gives an earlier use-by date or a shorter limit after opening, follow that instead. Use a clean spoon each time.