Meanwhile, place 1 tablespoon of the tahini in a small bowl. Squeeze the juice from one lemon half (about 1 1/2 tablespoons) into the bowl, season with the remaining 1/4 teaspoon kosher salt, and whisk until lightened in color, creamy, smooth, and pourable. The mixture might seize during whisking, but this is normal. Continue to whisk and it will smooth out. Crumble 2 ounces feta cheese (about 1/2 cup). Pick the leaves from 3 sprigs fresh oregano or thyme, if using, and coarsely chop the oregano leaves if large.
Dining and Cooking