Preheat your oven to 350°F (175°C). Grease the loaf pan or line it with parchment paper for easy removal.
In a large mixing bowl, combine the grated zucchini and salt. Allow it to sit for about 10 minutes, then squeeze out excess moisture using a clean kitchen towel.
In the bowl, whisk together the flour, baking powder, baking soda, garlic powder, black pepper, and dried oregano.
In another bowl, mix the eggs, vegetable oil, and milk until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the grated zucchini and shredded cheddar cheese until evenly distributed.
Pour the batter into the prepared loaf pan, smoothing the top with a spatula.
Bake in the preheated oven for about 50 minutes, or until a toothpick inserted in the center comes out clean.
Let the bread cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.