Line a colander with two layers of cheesecloth and place over a medium bowl. Place the yogurt on the cheesecloth and cover the colander with plastic wrap. Allow yogurt to drain 8 hours or overnight.
Scoop the drained yogurt into a mixing bowl. Mash the garlic cloves with the salt into a fine paste; mix into the yogurt. Stir the dill, parsley, and cream cheese into the yogurt and garlic mixture. Spread onto a dish and garnish with the mint leaves to serve.