Preheat your oven to 350°F (175°C). Grease your loaf pan or line it with parchment paper.
In a large mixing bowl, sprinkle the grated zucchini with salt and let it sit for about 5-10 minutes to draw out moisture.
After 10 minutes, place the zucchini in a clean kitchen towel and wring it out to remove excess moisture. Set aside.
In the same bowl, whisk together the eggs and vegetable oil until combined.
Add the drained zucchini to the egg mixture and stir well.
In another bowl, mix together the flour, cornmeal, sugar, baking powder, garlic powder, black pepper, and cayenne pepper (if using).
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Be careful not to overmix.
Fold in the shredded cheese and green onions (if using) into the batter.
Pour the batter into the prepared loaf pan, smoothing the top with a spatula.
Bake in the preheated oven for 45 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let it cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.