Place a sieve lined with two layers of cheesecloth inside a deep bowl. Mix the yogurt and salt together and pour into sieve, cover with cheesecloth, and place in the refrigerator for a minimum of 1 day and up to 3 days.
Using your hands, lightly squeeze yogurt to remove excess liquid. Unwrap cheesecloth and roll yogurt into small log.
Place shaped lebneh onto plate, drizzle with oil, sprinkle with mint, and season with freshly cracked pepper.