Combine eggs, oil, yogurt, vanilla, sugar and brown sugar in a mixing bowl and stir until smooth. Add in zucchini and mix till combined...Make sure you gave it a squeeze or patted it down with paper towels. You just want to get 75% of the moisture out of it.
Add in flour, baking soda, baking powder, salt (and a few dashes of cinnamon if you like) and mix until smooth.
Grease a cast iron skillet, cake pan or loaf pan, pour batter into it and bake for 30-45 minutes (depending on pan) until a toothpick inserted comes out clean.