Fold a piece of cheesecloth into 8 layers and place it in a large sieve set over a deep nonreactive bowl. (Or, for serious Bulgarian street cred, tie the ends of the cheesecloth around the handle of a spoon after you’ve added the yogurt and set it over the rim of a large glass jar so it can drip freely.)
In a bowl, combine yogurt with 11⁄2 tsp. kosher salt. Pour yogurt into the cheesecloth, cover the sieve loosely with plastic, and let sit overnight at room temperature, giving the yogurt plenty of time to drain off its excess water. (The yogurt is super acidic and cultured, so it won’t go bad, but if this makes you squeamish, put it in the fridge; just allow twice as long for it to drain.)
After 12 to 15 hours, you should have 2 to 3 cups of thick, very creamy labneh remaining in the cheesecloth and at least 5 cups of whey in the bowl. Use a spatula to scrape the labneh into a container, then set it aside at room temperature if you’re about to serve it; otherwise, cover and refrigerate (it will keep for up to 2 weeks).
Spread the labneh on a serving platter or in a wide, shallow bowl, making wells in the center so the cheese comes up the sides of the bowl a bit. Add the olive oil, and onion slices (or radishes, if using); garnish mint leaves and pomegranate seeds, if using, and finish with a generous pinch of flaky sea salt. Serve with plenty of bread for dipping.