1. In a medium bowl, stir together yogurt and salt. (If using store-bought labneh, skip to step 2.) Line a fine-mesh sieve with 2 layers of cheesecloth (allowing extra to drape over sieve); place sieve over a deep bowl or large (8-cup) liquid measure. Transfer yogurt to prepared sieve. Gather edges of cheesecloth around yogurt mixture; tie with kitchen twine. Transfer bowl, sieve, and yogurt to refrigerator; drain 12 hours (discarding liquid occasionally to make sure liquid collected from yogurt in bowl doesn't touch sieve). Remove yogurt cheese from cheesecloth.
2. Use clean hands to roll cheese into 1-inch balls (about 1 rounded tablespoon each). Meanwhile, heat oil in a small skillet over medium heat; add oregano and cook until crisp and fragrant (about 1 minute). Cool oil and oregano completely (discarding darkened oregano, if desired) and pour over yogurt cheese to serve. Garnish with fresh oregano.
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