Preheat the oven to 350˚F. Coat the interior of a 12-inch skillet with cooking spray. (Cast iron works well.)
Grate the zucchini on the large holes of a box grater. Squeeze out some of the moisture.
Whisk the eggs in a large bowl; add the oil, yogurt, sugar; mix thoroughly and stir in the zucchini.
In a second bowl, combine the flour, salt, baking soda and baking powder. Use a rubber spatula to stir it into the wet mixture, but stir only until the ingredients are incorporated. (Over stirring will make the cake tough.)
Transfer the batter to the prepared pan and bake, rotating the pan once in the oven, until a toothpick inserted in the center comes out nearly dry, about 1 hour.
Nutritional analysis for each serving: 288 calories, 5 g protein, 33 g carbohydrates, 1 g fiber, 16 g fat, 2 g saturated fat, 322 mg sodium