Place grated zucchini in a colander. Lightly sprinkle with salt and let stand for 20 minutes. After 20 minutes, gently press down on the zucchini to remove any excess liquid.
In a large bowl, combine zucchini, egg, yogurt, cheese, and cayenne. Stir to combine.
Stir flour and baking powder together in a small bowl, then add to zucchini mixture. Add salt and pepper to taste, and combine all ingredients well.
Pour enough olive oil into a skillet to thinly coat the bottom. Place on medium-high heat and fry the pancakes. Flip when golden brown on bottom, after about 4 minutes. Cook on the other side for another 2 minutes, or until golden.