Line a strainer with a layer of cheesecloth or a coffee filter and place over a bowl. Add the yogurt, refrigerate, and let drain until thick and reduced to 1 cup, 2 to 3 hours. Discard the liquid in the bowl or reserve for another use, such as bread making.
In a blender, combine the feta, oil, garlic, lemon juice, salt, and cayenne, and process until smooth, adding more oil 1/2 teaspoon at a time if needed. Add the strained yogurt and pulse to combine. Add the mint leaves and Essence. Adjust the seasoning, to taste.
Cover and refrigerate until ready to serve.
Yield: about 1 1/4 cups